/* * /MathJax/config/TeX-MML-AM_SVG-full.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.Ajax.Preloading( "[MathJax]/jax/input/TeX/config.js", "[MathJax]/jax/input/MathML/config.js", "[MathJax]/jax/input/AsciiMath/config.js", "[MathJax]/jax/output/SVG/config.js", "[MathJax]/jax/output/PreviewHTML/config.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/SVG/jax.js", "[MathJax]/jax/output/SVG/autoload/mtable.js", "[MathJax]/jax/output/PreviewHTML/jax.js", "[MathJax]/extensions/fast-preview.js", "[MathJax]/extensions/AssistiveMML.js" ); MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.9",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:"2.7.9",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:"2.7.9",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.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.9",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_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",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.9",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); MathJax.Extension.tex2jax={version:"2.7.9",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); MathJax.Extension.asciimath2jax={version:"2.7.9",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); (function(f,o,q,e,r){var p="2.7.9";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},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(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}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(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.9";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); (function(b,e){var d="2.7.9";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); MathJax.Extension["TeX/noUndefined"]={version:"2.7.9",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); (function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{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",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],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:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],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",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["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",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","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:["CrLaTeX",true],hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\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"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);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)||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[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].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;r0){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[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=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 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(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].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[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);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[g]});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=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=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(/^[a-z]+:/,"")==="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="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h&&(ai.input.length>1||ag.ttype==b)){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o}}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.9";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); (function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-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",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.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[q];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[n.mathvariant]}},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=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(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].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[o]&&this.data[o].PHTML){return this.data[o].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[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/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[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){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[r];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(r){o.style.marginRight=g.Em(r)}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[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];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[this.over]){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[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].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[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].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[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];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(r);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){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[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].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(r);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;ps){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/g,"")}catch(l){g.copyAttributes.id=true;if(!l.restart){throw l}return MathJax.Callback.After(["HandleMML",this,n],l.restart)}o.setAttribute("data-mathml",j);k=f.addElement(o,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(i.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{k.innerHTML=j}catch(l){}o.style.position="relative";o.setAttribute("role","presentation");o.firstChild.setAttribute("aria-hidden","true");k.setAttribute("role","presentation")}n.i++}g.copyAttributes.id=true;n.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_SVG-full.js");