2 * /MathJax/config/TeX-AMS_HTML.js
4 * Copyright (c) 2010-11 Design Science, Inc.
6 * Part of the MathJax library.
7 * See http://www.mathjax.org for details.
9 * Licensed under the Apache License, Version 2.0;
10 * you may not use this file except in compliance with the License.
12 * http://www.apache.org/licenses/LICENSE-2.0
15 MathJax
.Ajax
.Preloading(
16 "[MathJax]/jax/input/TeX/config.js",
17 "[MathJax]/jax/output/HTML-CSS/config.js",
18 "[MathJax]/extensions/tex2jax.js",
19 "[MathJax]/extensions/MathZoom.js",
20 "[MathJax]/extensions/MathMenu.js",
21 "[MathJax]/jax/element/mml/jax.js",
22 "[MathJax]/extensions/toMathML.js",
23 "[MathJax]/extensions/TeX/noErrors.js",
24 "[MathJax]/extensions/TeX/noUndefined.js",
25 "[MathJax]/jax/input/TeX/jax.js",
26 "[MathJax]/extensions/TeX/AMSmath.js",
27 "[MathJax]/extensions/TeX/AMSsymbols.js"
30 MathJax
.Hub
.Config({"v1.0-compatible":false});
32 MathJax
.InputJax
.TeX
=MathJax
.InputJax({id
:"TeX",version
:"1.1.1",directory
:MathJax
.InputJax
.directory
+"/TeX",extensionDir
:MathJax
.InputJax
.extensionDir
+"/TeX",config
:{TagSide
:"right",TagIndent
:"0.8em",MultLineWidth
:"85%"}});MathJax
.InputJax
.TeX
.Register("math/tex");MathJax
.InputJax
.TeX
.loadComplete("config.js");
34 MathJax
.OutputJax
["HTML-CSS"]=MathJax
.OutputJax({id
:"HTML-CSS",version
:"1.1.5",directory
:MathJax
.OutputJax
.directory
+"/HTML-CSS",extensionDir
:MathJax
.OutputJax
.extensionDir
+"/HTML-CSS",autoloadDir
:MathJax
.OutputJax
.directory
+"/HTML-CSS/autoload",fontDir
:MathJax
.OutputJax
.directory
+"/HTML-CSS/fonts",webfontDir
:MathJax
.OutputJax
.fontDir
+"/HTML-CSS",config
:{scale
:100,minScaleAdjust
:50,availableFonts
:["STIX","TeX"],preferredFont
:"TeX",webFont
:"TeX",imageFont
:"TeX",undefinedFamily
:"STIXGeneral,'Arial Unicode MS',serif",showMathMenu
:true,styles
:{".MathJax_Display":{"text-align":"center",margin
:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color
:"#CC0000",border
:"1px solid #CC0000",padding
:"1px 3px","font-family":"serif","font-style":"normal","font-size":"90%"},".MathJax_Preview":{color
:"#888888"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color
:"InfoText",border
:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter
:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding
:"3px 4px"}}}});if(MathJax
.Hub
.Browser
.isMSIE
&&document
.documentMode
>=9){delete MathJax
.OutputJax
["HTML-CSS"].config
.styles
["#MathJax_Tooltip"].filter
}if(!MathJax
.Hub
.config
.delayJaxRegistration
){MathJax
.OutputJax
["HTML-CSS"].Register("jax/mml")}MathJax
.Hub
.Register
.StartupHook("End Config",[function(b
,c
){var a
=b
.Insert({minBrowserVersion
:{Firefox
:3,Opera
:9.52,MSIE
:6,Chrome
:0.3,Safari
:2,Konqueror
:4},inlineMathDelimiters
:["$","$"],displayMathDelimiters
:["$$","$$"],multilineDisplay
:true,minBrowserTranslate:function(f
){var e
=b
.getJaxFor(f
),k
=["[Math]"],j
;var h
=document
.createElement("span",{className
:"MathJax_Preview"});if(e
.inputJax
.id
==="TeX"){if(e
.root
.Get("displaystyle")){j
=a
.displayMathDelimiters
;k
=[j
[0]+e
.originalText
+j
[1]];if(a
.multilineDisplay
){k
=k
[0].split(/\n/)}}else{j
=a
.inlineMathDelimiters
;k
=[j
[0]+e
.originalText
.replace(/^\s+/,"").replace(/\s+$/,"")+j
[1]]}}for(var g
=0,d
=k
.length
;g
<d
;g
++){h
.appendChild(document
.createTextNode(k
[g
]));if(g
<d
-1){h
.appendChild(document
.createElement("br"))}}f
.parentNode
.insertBefore(h
,f
)}},(b
.config
["HTML-CSS"]||{}));if(b
.Browser
.version
!=="0.0"&&!b
.Browser
.versionAtLeast(a
.minBrowserVersion
[b
.Browser
]||0)){c
.Translate
=a
.minBrowserTranslate
;b
.Config({showProcessingMessages
:false});MathJax
.Message
.Set("Your browser does not support MathJax",null,4000);b
.Startup
.signal
.Post("MathJax not supported")}},MathJax
.Hub
,MathJax
.OutputJax
["HTML-CSS"]]);MathJax
.OutputJax
["HTML-CSS"].loadComplete("config.js");
36 MathJax
.Extension
.tex2jax
={version
:"1.1.3",config
:{inlineMath
:[["\\(","\\)"]],displayMath
:[["$$","$$"],["\\[","\\]"]],skipTags
:["script","noscript","style","textarea","pre","code"],ignoreClass
:"tex2jax_ignore",processClass
:"tex2jax_process",processEscapes
:false,processEnvironments
:true,preview
:"TeX"},PreProcess:function(a
){if(!this.configured
){this.config
=MathJax
.Hub
.CombineConfig("tex2jax",this.config
);if(this.config
.Augment
){MathJax
.Hub
.Insert(this,this.config
.Augment
)}if(typeof(this.config
.previewTeX
)!=="undefined"&&!this.config
.previewTeX
){this.config
.preview
="none"}this.configured
=true}if(typeof(a
)==="string"){a
=document
.getElementById(a
)}if(!a
){a
=document
.body
}this.createPatterns();this.scanElement(a
,a
.nextSibling
)},createPatterns:function(){var d
=[],c
,a
,b
=this.config
;this.match
={};for(c
=0,a
=b
.inlineMath
.length
;c
<a
;c
++){d
.push(this.patternQuote(b
.inlineMath
[c
][0]));this.match
[b
.inlineMath
[c
][0]]={mode
:"",end
:b
.inlineMath
[c
][1],pattern
:this.endPattern(b
.inlineMath
[c
][1])}}for(c
=0,a
=b
.displayMath
.length
;c
<a
;c
++){d
.push(this.patternQuote(b
.displayMath
[c
][0]));this.match
[b
.displayMath
[c
][0]]={mode
:"; mode=display",end
:b
.displayMath
[c
][1],pattern
:this.endPattern(b
.displayMath
[c
][1])}}this.start
=new RegExp(d
.sort(this.sortLength
).join("|")+(b
.processEnvironments
?"|\\\\begin\\{([^}]*)\\}":"")+(b
.processEscapes
?"|\\\\*\\\\\\$":""),"g");this.skipTags
=new RegExp("^("+b
.skipTags
.join("|")+")$","i");this.ignoreClass
=new RegExp("(^| )("+b
.ignoreClass
+")( |$)");this.processClass
=new RegExp("(^| )("+b
.processClass
+")( |$)")},patternQuote:function(a
){return a
.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a
){return new RegExp(this.patternQuote(a
)+"|\\\\.","g")},sortLength:function(d
,c
){if(d
.length
!==c
.length
){return c
.length
-d
.length
}return(d
==c
?0:(d
<c
?-1:1))},scanElement:function(c
,b
,f
){var a
,e
,d
;while(c
&&c
!=b
){if(c
.nodeName
.toLowerCase()==="#text"){if(!f
){c
=this.scanText(c
)}}else{a
=(typeof(c
.className
)==="undefined"?"":c
.className
);e
=(typeof(c
.tagName
)==="undefined"?"":c
.tagName
);if(typeof(a
)!=="string"){a
=String(a
)}if(c
.firstChild
&&!a
.match(/(^| )MathJax/)&&!this.skipTags
.exec(e
)){d
=(f
||this.ignoreClass
.exec(a
))&&!this.processClass
.exec(a
);this.scanElement(c
.firstChild
,b
,d
)}}if(c
){c
=c
.nextSibling
}}},scanText:function(b
){if(b
.nodeValue
.replace(/\s+/,"")==""){return b
}var a
,c
;this.search
={start
:true};this.pattern
=this.start
;while(b
){this.pattern
.lastIndex
=0;while(b
&&b
.nodeName
.toLowerCase()==="#text"&&(a
=this.pattern
.exec(b
.nodeValue
))){if(this.search
.start
){b
=this.startMatch(a
,b
)}else{b
=this.endMatch(a
,b
)}}if(this.search
.matched
){b
=this.encloseMath(b
)}if(b
){do{c
=b
;b
=b
.nextSibling
}while(b
&&(b
.nodeName
.toLowerCase()==="br"||b
.nodeName
.toLowerCase()==="#comment"));if(!b
||b
.nodeName
!=="#text"){return c
}}}return b
},startMatch:function(a
,b
){var f
=this.match
[a
[0]];if(f
!=null){this.search
={end
:f
.end
,mode
:f
.mode
,open
:b
,olen
:a
[0].length
,opos
:this.pattern
.lastIndex
-a
[0].length
};this.switchPattern(f
.pattern
)}else{if(a
[0].substr(0,6)==="\\begin"){this.search
={end
:"\\end{"+a
[1]+"}",mode
:"; mode=display",open
:b
,olen
:0,opos
:this.pattern
.lastIndex
-a
[0].length
,isBeginEnd
:true};this.switchPattern(this.endPattern(this.search
.end
))}else{var d
=a
[0].substr(0,a
[0].length
-1),g
,c
;if(d
.length
%2===0){c
=[d
.replace(/\\\\/g,"\\")];g=1}else{c=[d.substr(1).replace(/\\\\/g,"\\"),"$"];g=0}c=MathJax.HTML.Element("span",null,c);var e=MathJax.HTML.TextNode(b.nodeValue.substr(0,a.index));b.nodeValue=b.nodeValue.substr(a.index+a[0].length-g);b.parentNode.insertBefore(c,b);b.parentNode.insertBefore(e,c);this.pattern.lastIndex=g}}return b},endMatch:function(a,b){if(a[0]==this.search.end){this.search.close=b;this.search.cpos=this.pattern.lastIndex;this.search.clen=(this.search.isBeginEnd?0:a[0].length);this.search.matched=true;b=this.encloseMath(b);this.switchPattern(this.start)}return b},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA
\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b;if(this.config.preview==="TeX"){b=[this.filterTeX(a)]}else{if(this.config.preview instanceof Array){b=this.config.preview}}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex
"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterTeX:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess
",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax
]/extensions/tex2jax
.js
");
38 (function(a,c,e,b,h){var i="1.1";var g=a.CombineConfig("MathZoom
",{delay:400,styles:{"#MathJax_Zoom
":{position:"absolute
","background
-color
":"#F0F0F0
",overflow:"auto
",display:"block
","z
-index
":301,padding:".5em
",border:"1px solid black
",margin:0,"font
-family
":"serif
","font
-size
":"85%","font
-weight
":"normal
","font
-style
":"normal
","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
","box
-shadow
":"5px
5px
15px
#AAAAAA
","-webkit
-box
-shadow
":"5px
5px
15px
#AAAAAA
","-moz
-box
-shadow
":"5px
5px
15px
#AAAAAA
","-khtml
-box
-shadow
":"5px
5px
15px
#AAAAAA
",filter:"progid
:DXImageTransform
.Microsoft
.dropshadow(OffX
=2, OffY
=2, Color
='gray', Positive
='true')"},"#MathJax_ZoomOverlay
":{position:"absolute
",left:0,top:0,"z
-index
":300,display:"inline
-block
",width:"100%",height:"100%",border:0,padding:0,margin:0,"background
-color
":"white
",opacity:0,filter:"alpha(opacity
=0)"}}});var d=function(j){if(!j){j=window.event}if(j){if(j.preventDefault){j.preventDefault()}if(j.stopPropagation){j.stopPropagation()}j.cancelBubble=true;j.returnValue=false}return false};var f=MathJax.Extension.MathZoom={version:i,settings:a.config.menuSettings,HandleEvent:function(l,j,k){if(!l){l=window.event}if(f.settings.CTRL&&!l.ctrlKey){return true}if(f.settings.ALT&&!l.altKey){return true}if(f.settings.CMD&&!l.metaKey){return true}if(f.settings.Shift&&!l.shiftKey){return true}return f[j](l,k)},Click:function(k,j){if(this.settings.zoom==="Click
"){return this.Zoom(j,k)}},DblClick:function(k,j){if(this.settings.zoom==="Double
-Click
"){return this.Zoom(j,k)}},Mouseover:function(k,j){if(this.settings.zoom==="Hover
"){f.oldMouseOver=j.onmouseover;j.onmouseover=null;j.onmousemove=this.Mousemove;j.onmouseout=this.Mouseout;return f.Timer(k,j)}},Mouseout:function(j){this.onmouseover=f.oldMouseOver;delete f.oldMouseOver;this.onmousemove=this.onmouseout=null;f.ClearTimer();return d(j)},Mousemove:function(j){return f.Timer(j||window.event,this)},Timer:function(k,j){this.ClearTimer();this.timer=setTimeout(MathJax.Callback(["Zoom
",this,j,{}]),g.delay);return d(k)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer);delete this.timer}},Zoom:function(s,l){this.ClearTimer();this.Remove();var v=s.parentNode;if(v.className==="MathJax_MathContainer
"){v=v.parentNode}if(v.parentNode.className==="MathJax_MathContainer
"){v=v.parentNode.parentNode}var q=(String(v.className).match(/^MathJax_(MathML|Display)$/)?v:s).nextSibling;var m=a.getJaxFor(q),r=m.root;var o=(b&&m.outputJax.isa(b.constructor)?"HTMLCSS
":(h&&m.outputJax.isa(h.constructor)?"MathML
":null));if(!o){return}var j=Math.floor(0.85*document.body.clientWidth),p=Math.floor(0.85*document.body.clientHeight);var k=c.Element("span
",{style:{position:"relative
",display:"inline
-block
",height:0,width:0},id:"MathJax_ZoomFrame
"},[["span
",{id:"MathJax_ZoomOverlay
",onmousedown:this.Remove}],["span
",{id:"MathJax_Zoom
",onclick:this.Remove,style:{visibility:"hidden
",fontSize:this.settings.zscale,"max
-width
":j+"px
","max
-height
":p+"px
"}},[["span
"]]]]);var x=k.lastChild,u=x.firstChild,n=k.firstChild;s.parentNode.insertBefore(k,s);if(this.msieZIndexBug){var t=c.Element("img
",{src:"about
:blank
",id:"MathJax_ZoomTracker
",style:{width:0,height:0,position:"relative
"}});document.body.appendChild(k);k.style.position="absolute
";k.style.zIndex=g.styles["#MathJax_ZoomOverlay
"]["z
-index
"];k=t}var w=(this["Zoom
"+o])(r,u,s);if(this.msiePositionBug){if(this.msieIE8Bug){u.style.position="absolute
";x.style.height=u.offsetHeight;u.style.position="";if(x.offsetHeight<=p&&x.offsetWidth<=j){x.style.overflow="visible
"}}if(this.msieWidthBug){x.style.width=Math.min(j,w.w)}else{if(w.w>j){x.style.width=j}}if(x.offsetHeight>p){x.style.Height=p+"px
"}if(s.nextSibling){s.parentNode.insertBefore(k,s.nextSibling)}else{v.appendChild(k)}}else{if(this.operaPositionBug){x.style.width=Math.min(j,u.offsetWidth)+"px
"}}this.Position(x,w,(o==="MathML
"&&v.nodeName.toLowerCase()==="div
"));x.style.visibility="";if(this.settings.zoom==="Hover
"){n.onmouseover=this.Remove}if(window.addEventListener){addEventListener("resize
",this.Resize,false)}else{if(window.attachEvent){attachEvent("onresize
",this.Resize)}else{this.onresize=window.onresize;window.onresize=this.Resize}}return d(l)},ZoomHTMLCSS:function(o,q,p){q.className="MathJax
";b.idPostfix="-zoom
";b.getScales(q,q);o.toHTML(q,q);var r=o.HTMLspanElement().bbox;b.idPostfix="";if(r.width&&r.width!=="100%"){var j=Math.floor(0.85*document.body.clientWidth);q.style.width=j+"px
";q.style.display="inline
-block
";var k=(o.id||"MathJax
-Span
-"+o.spanID)+"-zoom
";var l=document.getElementById(k).firstChild;while(l&&l.style.width!==r.width){l=l.nextSibling}if(l){l.style.width="100%"}}q.appendChild(this.topImg);var n=this.topImg.offsetTop;q.removeChild(this.topImg);var m=(this.msieWidthBug?b.getW(p)*b.em:p.offsetWidth);return{w:r.w*b.em,Y:-n,W:m}},ZoomMathML:function(k,l,m){k.toNativeMML(l,l);var n;l.appendChild(this.topImg);n=this.topImg.offsetTop;l.removeChild(this.topImg);var j=(this.ffMMLwidthBug?m.parentNode:m).offsetWidth;return{w:l.offsetWidth,Y:-n,W:j}},Position:function(p,n,r){var k=this.Resize(),m=k.x,l=k.y,j=n.W;if(this.msiePositionBug){j=-j}if(r&&this.ffMMLcenterBug){j=0}var q=-Math.floor((p.offsetWidth-j)/2),o=n.Y;p.style.left=Math.max(q,20-m)+"px
";p.style.top=Math.max(o,20-l)+"px
"},Resize:function(l){if(f.onresize){f.onresize(l)}var j=0,o=0,n=document.getElementById("MathJax_ZoomFrame
"),k=document.getElementById("MathJax_ZoomOverlay
");var m=(f.msieZIndexBug?document.getElementById("MathJax_ZoomTracker
"):n);if(f.operaPositionBug){n.style.border="1px solid
"}if(m.offsetParent){do{j+=m.offsetLeft;o+=m.offsetTop}while(m=m.offsetParent)}if(f.operaPositionBug){n.style.border=""}if(f.msieZIndexBug){n.style.left=j+"px
";n.style.top=o+"px
"}k.style.left=(-j)+"px
";k.style.top=(-o)+"px
";if(f.msiePositionBug){setTimeout(f.SetWH,0)}else{f.SetWH()}return{x:j,y:o}},SetWH:function(){var j=document.getElementById("MathJax_ZoomOverlay
");j.style.width=j.style.height="1px
";j.style.width=document.body.scrollWidth+"px
";j.style.height=document.body.scrollHeight+"px
"},Remove:function(k){var l=document.getElementById("MathJax_ZoomFrame
");if(l){l.parentNode.removeChild(l);l=document.getElementById("MathJax_ZoomTracker
");if(l){l.parentNode.removeChild(l)}if(f.operaRefreshBug){var j=c.addElement(document.body,"div
",{style:{position:"fixed
",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white
",opacity:0},id:"MathJax_OperaDiv
"});document.body.removeChild(j)}if(window.removeEventListener){removeEventListener("resize
",f.Resize,false)}else{if(window.detachEvent){detachEvent("onresize
",f.Resize)}else{window.onresize=f.onresize;delete f.onresize}}}return d(k)}};a.Register.StartupHook("HTML
-CSS Jax Ready
",function(){b=MathJax.OutputJax["HTML
-CSS
"];b.Augment({HandleEvent:f.HandleEvent})});a.Register.StartupHook("NativeMML Jax Ready
",function(){h=MathJax.OutputJax.NativeMML;h.Augment({HandleEvent:f.HandleEvent,MSIEmouseup:function(l,k,j){if(this.trapUp){delete this.trapUp;return true}if(this.MSIEzoomKeys(l)){return true}return false},MSIEclick:function(l,k,j){if(this.trapClick){delete this.trapClick;return true}if(!this.MSIEzoomKeys(l)){return false}if(!this.settings.zoom.match(/Click/)){return false}return(f.Click(l,k)===false)},MSIEdblclick:function(l,k,j){if(!this.MSIEzoomKeys(l)){return false}return(f.DblClick(l,k)===false)},MSIEmouseover:function(l,k,j){if(this.settings.zoom!=="Hover
"){return false}f.Timer(l,k);return true},MSIEmouseout:function(l,k,j){if(this.settings.zoom!=="Hover
"){return false}f.ClearTimer();return true},MSIEmousemove:function(l,k,j){if(this.settings.zoom!=="Hover
"){return false}f.Timer(l,k);return true},MSIEzoomKeys:function(j){if(this.settings.CTRL&&!j.ctrlKey){return false}if(this.settings.CMD&&!j.metaKey){return false}if(this.settings.ALT&&!j.altKey){return false}if(this.settings.Shift&&!j.shiftKey){return false}return true}})});a.Browser.Select({MSIE:function(j){var k=(document.compatMode==="BackCompat
");var l=j.versionAtLeast("8.0")&&document.documentMode>7;f.msiePositionBug=true;f.msieWidthBug=!k;f.msieIE8Bug=l;f.msieZIndexBug=!l;f.msieInlineBlockAlignBug=(!l||k);if(document.documentMode>=9){delete g.styles["#MathJax_Zoom
"].filter}},Opera:function(j){f.operaPositionBug=true;f.operaRefreshBug=true},Firefox:function(j){f.ffMMLwidthBug=true;f.ffMMLcenterBug=true}});f.topImg=(f.msieInlineBlockAlignBug?c.Element("img
",{style:{width:0,height:0},src:"about
:blank
"}):c.Element("span
",{style:{width:0,height:0,display:"inline
-block
"}}));if(f.operaPositionBug){f.topImg.style.border="1px solid
"}MathJax.Callback.Queue(["Styles
",e,g.styles],["Post
",a.Startup.signal,"MathZoom Ready
"],["loadComplete
",e,"[MathJax
]/extensions
/MathZoom
.js
"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML
-CSS
"],MathJax.OutputJax.NativeMML);
40 (function(b,c,f){var k="1.1.4";MathJax.Extension.MathMenu={version:k};var i=b.Browser.isPC,g=b.Browser.isMSIE;var e=(i?null:"5px
");var j=b.CombineConfig("MathMenu
",{delay:150,helpURL:"http
://www.mathjax.org/help/user/",showRenderer:true,showFontMenu:false,showContext:false,windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:100,height:50},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_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(i?"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":e,"-webkit-border-radius":e,"-moz-border-radius":e,"-khtml-border-radius":e,"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:(i?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuTitle":{"background-color":"#CCCCCC",margin:(i?"-1px -1px 1px -1px":"-5px 0 0 0"),"text-align":"center","font-style":"italic","font-size":"80%",color:"#444444",padding:"2px 0",overflow:"hidden"},".MathJax_MenuArrow":{position:"absolute",right:".5em",color:"#666666","font-family":(g?"'Arial unicode MS'":null)},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(g?"'Arial unicode MS'":null)},".MathJax_MenuRadioCheck":{position:"absolute",left:(i?"1em":".7em")},".MathJax_MenuLabel":{padding:(i?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(i?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(i?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(i?"Highlight":"#606872"),color:(i?"HighlightText":"white")}}});var d=function(l){if(!l){l=window.event}if(l){if(l.preventDefault){l.preventDefault()}if(l.stopPropagation){l.stopPropagation()}l.cancelBubble=true;l.returnValue=false}return false};var a=MathJax.Menu=MathJax.Object.Subclass({version:k,items:[],posted:false,title:null,margin:5,Init:function(l){this.items=[].slice.call(arguments,0)},With:function(l){if(l){b.Insert(this,l)}return this},Post:function(n,v){if(!n){n=window.event}var t=(!this.title?null:[["div",{className:"MathJax_MenuTitle"},[this.title]]]);var l=document.getElementById("MathJax_MenuFrame");if(!l){l=a.Background(this)}var o=c.addElement(l,"div",{onmouseup:a.Mouseup,ondblclick:this.False,ondragstart:this.False,onselectstart:this.False,oncontextmenu:this.False,menuItem:this,className:"MathJax_Menu"},t);for(var q=0,p=this.items.length;q<p;q++){this.items[q].Create(o)}this.posted=true;o.style.width=(o.offsetWidth+2)+"px";var u=n.pageX,s=n.pageY;if(!u&&!s){u=n.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;s=n.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!v){if(u+o.offsetWidth>document.body.offsetWidth-this.margin){u=document.body.offsetWidth-o.offsetWidth-this.margin}a.skipUp=true}else{var r="left",w=v.offsetWidth;u=v.offsetWidth-2;s=0;while(v&&v!==l){u+=v.offsetLeft;s+=v.offsetTop;v=v.parentNode}if(u+o.offsetWidth>document.body.offsetWidth-this.margin){r="right";u=Math.max(this.margin,u-w-o.offsetWidth+6)}if(!i){o.style["borderRadiusTop"+r]=0;o.style["WebkitBorderRadiusTop"+r]=0;o.style["MozBorderRadiusTop"+r]=0;o.style["KhtmlBorderRadiusTop"+r]=0}}o.style.left=u+"px";o.style.top=s+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return this.False(n)},Remove:function(l,m){var n=document.getElementById("MathJax_MenuFrame");if(n){n.parentNode.removeChild(n);if(this.msieBackgroundBug){detachEvent("onresize",a.Resize)}}},Mouseup:function(l,m){if(a.skipUp){delete a.skipUp}else{this.Remove(l,m)}},False:d},{config:j,div:null,Remove:function(l){a.Event(l,this,"Remove")},Mouseover:function(l){a.Event(l,this,"Mouseover")},Mouseout:function(l){a.Event(l,this,"Mouseout")},Mousedown:function(l){a.Event(l,this,"Mousedown")},Mouseup:function(l){a.Event(l,this,"Mouseup")},Mousemove:function(l){a.Event(l,this,"Mousemove")},Event:function(n,o,l){if(!n){n=window.event}var m=o.menuItem;if(m&&m[l]){return m[l](n,o)}return null},BGSTYLE:{position:"absolute",left:0,top:0,"z-index":200,width:"100%",height:"100%",border:0,padding:0,margin:0},Background:function(m){var n=c.addElement(document.body,"div",{style:this.BGSTYLE,id:"MathJax_MenuFrame"},[["div",{style:this.BGSTYLE,menuItem:m,onmousedown:this.Remove}]]);var l=n.firstChild;if(m.msieBackgroundBug){l.style.backgroundColor="white";l.style.filter="alpha(opacity=0)";n.width=n.height=0;this.Resize();attachEvent("onresize",this.Resize)}else{l.style.position="fixed"}return n},Resize:function(){setTimeout(a.SetWH,0)},SetWH:function(){var l=document.getElementById("MathJax_MenuFrame");if(l){l=l.firstChild;l.style.width=l.style.height="1px";l.style.width=document.body.scrollWidth+"px";l.style.height=document.body.scrollHeight+"px"}},saveCookie:function(){c.Cookie.Set("menu",this.cookie)},getCookie:function(){this.cookie=c.Cookie.Get("menu")}});var h=a.ITEM=MathJax.Object.Subclass({name:"",Create:function(m){if(!this.hidden){var l={onmouseover:a.Mouseover,onmouseout:a.Mouseout,onmouseup:a.Mouseup,onmousedown:this.False,ondragstart:this.False,onselectstart:this.False,onselectend:this.False,className:"MathJax_MenuItem",menuItem:this};if(this.disabled){l.className+=" MathJax_MenuDisabled"}c.addElement(m,"div",l,this.Label(l,m))}},Mouseover:function(q,s){if(!this.disabled){this.Activate(s)}if(!this.menu||!this.menu.posted){var r=document.getElementById("MathJax_MenuFrame").childNodes,n=s.parentNode.childNodes;for(var o=0,l=n.length;o<l;o++){var p=n[o].menuItem;if(p&&p.menu&&p.menu.posted){p.Deactivate(n[o])}}l=r.length-1;while(l>=0&&s.parentNode.menuItem!==r[l].menuItem){r[l].menuItem.posted=false;r[l].parentNode.removeChild(r[l]);l--}if(this.Timer){this.Timer(q,s)}}},Mouseout:function(l,m){if(!this.menu||!this.menu.posted){this.Deactivate(m)}if(this.timer){clearTimeout(this.timer);delete this.timer}},Mouseup:function(l,m){return this.Remove(l,m)},Remove:function(l,m){m=m.parentNode.menuItem;return m.Remove(l,m)},Activate:function(l){this.Deactivate(l);l.className+=" MathJax_MenuActive"},Deactivate:function(l){l.className=l.className.replace(/ MathJax_MenuActive/,"")},With:function(l){if(l){b.Insert(this,l)}return this},False:d});a.ITEM.COMMAND=a.ITEM.Subclass({action:function(){},Init:function(l,n,m){this.name=l;this.action=n;this.With(m)},Label:function(l,m){return[this.name]},Mouseup:function(l,m){if(!this.disabled){this.Remove(l,m);this.action.call(this,l)}return this.False(l)}});a.ITEM.SUBMENU=a.ITEM.Subclass({menu:null,marker:(i&&!b.Browser.isSafari?"\u25B6":"\u25B8"),Init:function(l,n){this.name=l;var m=1;if(!(n instanceof a.ITEM)){this.With(n),m++}this.menu=a.apply(a,[].slice.call(arguments,m))},Label:function(l,m){l.onmousemove=a.Mousemove;this.menu.posted=false;return[this.name+" ",["span",{className:"MathJax_MenuArrow"},[this.marker]]]},Timer:function(l,m){if(this.timer){clearTimeout(this.timer)}l={clientX:l.clientX,clientY:l.clientY};this.timer=setTimeout(MathJax.Callback(["Mouseup",this,l,m]),j.delay)},Mouseup:function(n,p){if(!this.disabled){if(!this.menu.posted){if(this.timer){clearTimeout(this.timer);delete this.timer}this.menu.Post(n,p)}else{var o=document.getElementById("MathJax_MenuFrame").childNodes,l=o.length-1;while(l>=0){var q=o[l];q.menuItem.posted=false;q.parentNode.removeChild(q);if(q.menuItem===this.menu){break}l--}}}return this.False(n)}});a.ITEM.RADIO=a.ITEM.Subclass({variable:null,marker:(i?"\u25CF":"\u2713"),Init:function(m,l,n){this.name=m;this.variable=l;this.With(n);if(this.value==null){this.value=this.name}},Label:function(m,n){var l={className:"MathJax_MenuRadioCheck"};if(j.settings[this.variable]!==this.value){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(p,q){if(!this.disabled){var r=q.parentNode.childNodes;for(var n=0,l=r.length;n<l;n++){var o=r[n].menuItem;if(o&&o.variable===this.variable){r[n].firstChild.style.display="none"}}q.firstChild.display="";j.settings[this.variable]=this.value;a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(p,q);return this.False(p)}});a.ITEM.CHECKBOX=a.ITEM.Subclass({variable:null,marker:"\u2713",Init:function(m,l,n){this.name=m;this.variable=l;this.With(n)},Label:function(m,n){var l={className:"MathJax_MenuCheck"};if(!j.settings[this.variable]){l={style:{display:"none"}}}return[["span",l,[this.marker]]," "+this.name]},Mouseup:function(l,m){if(!this.disabled){m.firstChild.display=(j.settings[this.variable]?"none":"");j.settings[this.variable]=!j.settings[this.variable];a.cookie[this.variable]=j.settings[this.variable];a.saveCookie();if(this.action){this.action.call(a)}}this.Remove(l,m);return this.False(l)}});a.ITEM.LABEL=a.ITEM.Subclass({Init:function(l,m){this.name=l;this.With(m)},Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuLabel";return[this.name]}});a.ITEM.RULE=a.ITEM.Subclass({Label:function(l,m){delete l.onmouseover,delete l.onmouseout;delete l.onmousedown;l.className+=" MathJax_MenuRule";return null}});a.About=function(){var o=MathJax.OutputJax["HTML-CSS"]||{fontInUse:""};var q=(o.webFonts?"":"local "),m=(o.webFonts?" web":"");var n=(o.imgFonts?"Image":q+o.fontInUse+m)+" fonts";var l=["MathJax.js v"+MathJax.fileversion,["br"]];l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(l,MathJax.InputJax,"Input Jax");a.About.GetJax(l,MathJax.OutputJax,"Output Jax");a.About.GetJax(l,MathJax.ElementJax,"Element Jax");l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}]);a.About.GetJax(l,MathJax.Extension,"Extension",true);l.push(["div",{style:{"border-top":"groove 2px",margin:".25em 0"}}],["center",{},[b.Browser+" v"+b.Browser.version+(o.webFonts?" \u2014 "+o.allowWebFonts+" fonts":"")]]);a.About.div=a.Background(a.About);var r=MathJax.HTML.addElement(a.About.div,"div",{id:"MathJax_About",onclick:a.About.Remove},[["b",{style:{fontSize:"120%"}},["MathJax"]]," v"+MathJax.version,["br"],"using "+n,["br"],["br"],["span",{style:{display:"inline-block","text-align":"left","font-size":"80%","background-color":"#E4E4E4",padding:".4em .6em",border:"1px inset"}},l],["br"],["br"],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]]]);var s=(document.documentElement||{});var p=window.innerHeight||s.clientHeight||s.scrollHeight||0;if(a.prototype.msieAboutBug){r.style.width="20em";r.style.position="absolute";r.style.left=Math.floor((document.documentElement.scrollWidth-r.offsetWidth)/2)+"px";r.style.top=(Math.floor((p-r.offsetHeight)/3)+document.body.scrollTop)+"px"}else{r.style.marginLeft=Math.floor(-r.offsetWidth/2)+"px";r.style.top=Math.floor((p-r.offsetHeight)/3)+"px"}};a.About.Remove=function(l){if(a.About.div){document.body.removeChild(a.About.div);delete a.About.div}};a.About.GetJax=function(l,o,n,m){for(var p in o){if(o.hasOwnProperty(p)&&o[p]){if((m&&o[p].version)||(o[p].isa&&o[p].isa(o))){l.push((o[p].id||p)+" "+n+" v"+o[p].version,["br"])}}}return l};a.Help=function(){window.open(j.helpURL,"MathJaxHelp")};a.ShowSource=function(o){if(!o){o=window.event}var n={screenX:o.screenX,screenY:o.screenY};if(!a.jax){return}if(j.settings.format==="MathML"){var l=MathJax.ElementJax.mml;if(l&&typeof(l.mbase.prototype.toMathML)!=="undefined"){try{a.ShowSource.Text(a.jax.root.toMathML(),o)}catch(m){if(!m.restart){throw m}MathJax.Callback.After([this,arguments.callee,n])}}else{if(!f.loadingToMathML){f.loadingToMathML=true;a.ShowSource.Window(o);MathJax.Callback.Queue(f.Require("[MathJax]/extensions/toMathML.js"),function(){delete f.loadingToMathML},[this,arguments.callee,n]);return}}}else{if(a.jax.originalText==null){alert("No TeX form available");return}a.ShowSource.Text(a.jax.originalText,o)}};a.ShowSource.Window=function(m){if(!a.ShowSource.w){var n=[],l=j.windowSettings;for(var o in l){if(l.hasOwnProperty(o)){n.push(o+"="+l[o])}}a.ShowSource.w=window.open("","_blank",n.join(","))}return a.ShowSource.w};a.ShowSource.Text=function(r,q){var n=a.ShowSource.Window(q);r=r.replace(/^\s*/,"").replace(/\s*$/,"");r=r.replace(/&/g,"&").replace(/</g,"<").replace(/>/g,">");n.document.open();n.document.write("<html><head><title>MathJax Equation Source</title></head><body style='font-size:85%'>");n.document.write("<table><tr><td><pre>"+r+"</pre></td></tr></table>");n.document.write("</body></html>");n.document.close();var p=n.document.body.firstChild;var o=(n.outerHeight-n.innerHeight)||30,m=(n.outerWidth-n.innerWidth)||30;m=Math.min(Math.floor(0.5*screen.width),p.offsetWidth+m+25);o=Math.min(Math.floor(0.5*screen.height),p.offsetHeight+o+25);n.resizeTo(m,o);if(q&&q.screenX!=null){var l=Math.max(0,Math.min(q.screenX-Math.floor(m/2),screen.width-m-20)),s=Math.max(0,Math.min(q.screenY-Math.floor(o/2),screen.height-o-20));n.moveTo(l,s)}delete a.ShowSource.w};a.Scale=function(){var m=MathJax.OutputJax["HTML-CSS"],l=MathJax.OutputJax.NativeMML;var o=(m?m.config.scale:l.config.scale);var n=prompt("Scale all mathematics (compared to surrounding text) by",o+"%");if(n){if(n.match(/^\s*\d+\s*%?\s*$/)){n=parseInt(n);if(n){if(n!==o){if(m){m.config.scale=n}if(l){l.config.scale=n}a.cookie.scale=n;a.saveCookie();b.Reprocess()}}else{alert("The scale should not be zero")}}else{alert("The scale should be a perentage (e.g., 120%)")}}};a.Zoom=function(){if(!MathJax.Extension.MathZoom){f.Require("[MathJax]/extensions/MathZoom.js")}};a.Renderer=function(){var l=b.config.outputJax["jax/mml"];if(l[0]!==j.settings.renderer){MathJax.Callback.Queue(["Require",f,"[MathJax]/jax/output/"+j.settings.renderer+"/config.js"],["Post",b.Startup.signal,j.settings.renderer+" output selected"],[function(){var p=MathJax.OutputJax[j.settings.renderer];for(var o=0,n=l.length;o<n;o++){if(l[o]===p){l.splice(o,1);break}}l.unshift(p)}],["Reprocess",b])}};a.Font=function(){var l=MathJax.OutputJax["HTML-CSS"];if(!l){return}document.location.reload()};b.Browser.Select({MSIE:function(l){var m=(document.compatMode==="BackCompat");var n=l.versionAtLeast("8.0")&&document.documentMode>7;a.Augment({margin:20,msieBackgroundBug:(m||!n),msieAboutBug:m});if(document.documentMode>=9){delete j.styles["#MathJax_About"].filter;delete j.styles[".MathJax_Menu"].filter}}});b.Register.StartupHook("End Config",function(){j.settings=b.config.menuSettings;if(!j.settings.format){j.settings.format=(MathJax.InputJax.TeX?"Original":"MathML")}if(typeof(j.settings.showRenderer)!=="undefined"){j.showRenderer=j.settings.showRenderer}if(typeof(j.settings.showFontMenu)!=="undefined"){j.showFontMenu=j.settings.showFontMenu}if(typeof(j.settings.showContext)!=="undefined"){j.showContext=j.settings.showContext}a.getCookie();a.menu=a(h.COMMAND("Show Source",a.ShowSource),h.SUBMENU("Format",h.RADIO("MathML","format"),h.RADIO("Original","format",{value:"Original"})),h.RULE(),h.SUBMENU("Settings",h.SUBMENU("Zoom Trigger",h.RADIO("Hover","zoom",{action:a.Zoom}),h.RADIO("Click","zoom",{action:a.Zoom}),h.RADIO("Double-Click","zoom",{action:a.Zoom}),h.RADIO("No Zoom","zoom",{value:"None"}),h.RULE(),h.LABEL("Trigger Requires:"),h.CHECKBOX((b.Browser.isMac?"Option":"Alt"),"ALT"),h.CHECKBOX("Command","CMD",{hidden:!b.Browser.isMac}),h.CHECKBOX("Control","CTRL",{hidden:b.Browser.isMac}),h.CHECKBOX("Shift","Shift")),h.SUBMENU("Zoom Factor",h.RADIO("125%","zscale"),h.RADIO("133%","zscale"),h.RADIO("150%","zscale"),h.RADIO("175%","zscale"),h.RADIO("200%","zscale"),h.RADIO("250%","zscale"),h.RADIO("300%","zscale"),h.RADIO("400%","zscale")),h.RULE(),h.SUBMENU("Math Renderer",{hidden:!j.showRenderer},h.RADIO("HTML-CSS","renderer",{action:a.Renderer}),h.RADIO("MathML","renderer",{action:a.Renderer,value:"NativeMML"})),h.SUBMENU("Font Preference",{hidden:!j.showFontMenu},h.LABEL("For HTML-CSS:"),h.RADIO("Auto","font",{action:a.Font}),h.RULE(),h.RADIO("TeX (local)","font",{action:a.Font}),h.RADIO("TeX (web)","font",{action:a.Font}),h.RADIO("TeX (image)","font",{action:a.Font}),h.RULE(),h.RADIO("STIX (local)","font",{action:a.Font})),h.SUBMENU("Contextual Menu",{hidden:!j.showContext},h.RADIO("MathJax","context"),h.RADIO("Browser","context")),h.COMMAND("Scale All Math ...",a.Scale)),h.RULE(),h.COMMAND("About MathJax",a.About),h.COMMAND("MathJax Help",a.Help))});a.showRenderer=function(l){a.cookie.showRenderer=j.showRenderer=l;a.saveCookie();a.menu.items[3].menu.item[3].hidden=!l};a.showFontMenu=function(l){a.cookie.showFontMenu=j.showFontMenu=l;a.saveCookie();a.menu.items[3].menu.items[4].hidden=!l};a.showContext=function(l){a.cookie.showContext=j.showContext=l;a.saveCookie();a.menu.items[3].menu.items[5].hidden=!l};MathJax.Callback.Queue(["Styles",f,j.styles],["Post",b.Startup.signal,"MathMenu Ready"],["loadComplete",f,"[MathJax]/extensions/MathMenu.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax);
42 MathJax
.ElementJax
.mml
=MathJax
.ElementJax({mimeType
:"jax/mml"},{id
:"mml",version
:"1.1.1",directory
:MathJax
.ElementJax
.directory
+"/mml",extensionDir
:MathJax
.ElementJax
.extensionDir
+"/mml",optableDir
:MathJax
.ElementJax
.directory
+"/mml/optable"});MathJax
.ElementJax
.mml
.Augment({Init:function(){if(arguments
.length
===1&&arguments
[0].type
==="math"){this.root
=arguments
[0]}else{this.root
=MathJax
.ElementJax
.mml
.math
.apply(this,arguments
)}if(this.root
.mode
){if(!this.root
.display
&&this.root
.mode
==="display"){this.root
.display
="block"}delete this.root
.mode
}}},{INHERIT
:"_inherit_",AUTO
:"_auto_",SIZE
:{INFINITY
:"infinity",SMALL
:"small",NORMAL
:"normal",BIG
:"big"},COLOR
:{TRANSPARENT
:"transparent"},VARIANT
:{NORMAL
:"normal",BOLD
:"bold",ITALIC
:"italic",BOLDITALIC
:"bold-italic",DOUBLESTRUCK
:"double-struck",FRAKTUR
:"fraktur",BOLDFRAKTUR
:"bold-fraktur",SCRIPT
:"script",BOLDSCRIPT
:"bold-script",SANSSERIF
:"sans-serif",BOLDSANSSERIF
:"bold-sans-serif",SANSSERIFITALIC
:"sans-serif-italic",SANSSERIFBOLDITALIC
:"sans-serif-bold-italic",MONOSPACE
:"monospace",INITIAL
:"inital",TAILED
:"tailed",LOOPED
:"looped",STRETCHED
:"stretched",CALIGRAPHIC
:"-tex-caligraphic",OLDSTYLE
:"-tex-oldstyle"},FORM
:{PREFIX
:"prefix",INFIX
:"infix",POSTFIX
:"postfix"},LINEBREAK
:{AUTO
:"auto",NEWLINE
:"newline",NOBREAK
:"nobreak",GOODBREAK
:"goodbreak",BADBREAK
:"badbreak"},LINEBREAKSTYLE
:{BEFORE
:"before",AFTER
:"after",DUPLICATE
:"duplicate",INFIXLINBREAKSTYLE
:"infixlinebreakstyle"},INDENTALIGN
:{LEFT
:"left",CENTER
:"center",RIGHT
:"right",AUTO
:"auto",ID
:"id",INDENTALIGN
:"indentalign"},INDENTSHIFT
:{INDENTSHIFT
:"indentshift"},LINETHICKNESS
:{THIN
:"thin",MEDIUM
:"medium",THICK
:"thick"},NOTATION
:{LONGDIV
:"longdiv",ACTUARIAL
:"actuarial",RADICAL
:"radical",BOX
:"box",ROUNDEDBOX
:"roundedbox",CIRCLE
:"circle",LEFT
:"left",RIGHT
:"right",TOP
:"top",BOTTOM
:"bottom",UPDIAGONALSTRIKE
:"updiagonalstrike",DOWNDIAGONALSTRIKE
:"downdiagonalstrike",VERTICALSTRIKE
:"verticalstrike",HORIZONTALSTRIKE
:"horizontalstrike",MADRUWB
:"madruwb"},ALIGN
:{TOP
:"top",BOTTOM
:"bottom",CENTER
:"center",BASELINE
:"baseline",AXIS
:"axis",LEFT
:"left",RIGHT
:"right"},LINES
:{NONE
:"none",SOLID
:"solid",DASHED
:"dashed"},SIDE
:{LEFT
:"left",RIGHT
:"right",LEFTOVERLAP
:"leftoverlap",RIGHTOVERLAP
:"rightoverlap"},WIDTH
:{AUTO
:"auto",FIT
:"fit"},ACTIONTYPE
:{TOGGLE
:"toggle",STATUSLINE
:"statusline",TOOLTIP
:"tooltip",INPUT
:"input"},LENGTH
:{VERYVERYTHINMATHSPACE
:"veryverythinmathspace",VERYTHINMATHSPACE
:"verythinmathspace",THINMATHSPACE
:"thinmathspace",MEDIUMMATHSPACE
:"mediummathspace",THICKMATHSPACE
:"thickmathspace",VERYTHICKMATHSPACE
:"verythickmathspace",VERYVERYTHICKMATHSPACE
:"veryverythickmathspace",NEGATIVEVERYVERYTHINMATHSPACE
:"negativeveryverythinmathspace",NEGATIVEVERYTHINMATHSPACE
:"negativeverythinmathspace",NEGATIVETHINMATHSPACE
:"negativethinmathspace",NEGATIVEMEDIUMMATHSPACE
:"negativemediummathspace",NEGATIVETHICKMATHSPACE
:"negativethickmathspace",NEGATIVEVERYTHICKMATHSPACE
:"negativeverythickmathspace",NEGATIVEVERYVERYTHICKMATHSPACE
:"negativeveryverythickmathspace"},OVERFLOW
:{LINBREAK
:"linebreak",SCROLL
:"scroll",ELIDE
:"elide",TRUNCATE
:"truncate",SCALE
:"scale"},UNIT
:{EM
:"em",EX
:"ex",PX
:"px",IN
:"in",CM
:"cm",MM
:"mm",PT
:"pt",PC
:"pc"},TEXCLASS
:{ORD
:0,OP
:1,BIN
:2,REL
:3,OPEN
:4,CLOSE
:5,PUNCT
:6,INNER
:7,VCENTER
:8,NONE
:-1},PLANE1
:String
.fromCharCode(55349)});(function(a
){var d
=false;var b
=true;a
.mbase
=MathJax
.Object
.Subclass({type
:"base",isToken
:d
,defaults
:{mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
},noInherit
:{},Init:function(){this.data
=[];if(this.inferRow
&&!(arguments
.length
===1&&arguments
[0].inferred
)){this.Append(a
.mrow().With({inferred
:b
}))}this.Append
.apply(this,arguments
)},With:function(f
){for(var g
in f
){if(f
.hasOwnProperty(g
)){this[g
]=f
[g
]}}return this},Append:function(){if(this.inferRow
&&this.data
.length
){this.data
[0].Append
.apply(this.data
[0],arguments
)}else{for(var g
=0,f
=arguments
.length
;g
<f
;g
++){this.SetData(this.data
.length
,arguments
[g
])}}},SetData:function(f
,g
){if(g
!=null){if(!(g
instanceof a
.mbase
)){g
=(this.isToken
?a
.chars(g
):a
.mtext(g
))}g
.parent
=this;g
.setInherit(this.inheritFromMe
?this:this.inherit
)}this.data
[f
]=g
},Parent:function(){var f
=this.parent
;while(f
&&f
.inferred
){f
=f
.parent
}return f
},Get:function(g
,k
){if(typeof(this[g
])!=="undefined"){return this[g
]}var h
=this.Parent();if(h
&&h
["adjustChild_"+g
]!=null){return(h
["adjustChild_"+g
])(h
.childPosition(this))}var j
=this.inherit
;var f
=j
;while(j
){if(typeof(j
[g
])!=="undefined"){var i
=j
.noInherit
[this.type
];if(!(i
&&i
[g
])){return j
[g
]}}f
=j
;j
=j
.inherit
}if(!k
){if(this.defaults
[g
]===a
.AUTO
){return this.autoDefault(g
)}if(this.defaults
[g
]!==a
.INHERIT
&&this.defaults
[g
]!=null){return this.defaults
[g
]}if(f
){return f
.defaults
[g
]}}return null},hasValue:function(f
){return(this.Get(f
,true)!=null)},getValues:function(){var g
={};for(var h
=0,f
=arguments
.length
;h
<f
;h
++){g
[arguments
[h
]]=this.Get(arguments
[h
])}return g
},adjustChild_scriptlevel:function(f
){return this.Get("scriptlevel")},adjustChild_displaystyle:function(f
){return this.Get("displaystyle")},adjustChild_texprimestyle:function(f
){return this.Get("texprimestyle")},childPosition:function(h
){if(h
.parent
.inferred
){h
=h
.parent
}for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]===h
){return g
}}return null},setInherit:function(h
){if(h
!==this.inherit
&&this.inherit
==null){this.inherit
=h
;for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]&&this.data
[g
].setInherit
){this.data
[g
].setInherit(h
)}}}},setTeXclass:function(f
){this.getPrevClass(f
);return(typeof(this.texClass
)!=="undefined"?this:f
)},getPrevClass:function(f
){if(f
){this.prevClass
=f
.Get("texClass");this.prevLevel
=f
.Get("scriptlevel")}},updateTeXclass:function(f
){if(f
){this.prevClass
=f
.prevClass
;delete f
.prevClass
;this.prevLevel
=f
.prevLevel
;delete f
.prevLevel
;this.texClass
=f
.Get("texClass")}},texSpacing:function(){var g
=(this.prevClass
!=null?this.prevClass
:a
.TEXCLASS
.NONE
);var f
=(this.Get("texClass")||a
.TEXCLASS
.ORD
);if(g
===a
.TEXCLASS
.NONE
||f
===a
.TEXCLASS
.NONE
){return""}if(g
===a
.TEXCLASS
.VCENTER
){g
=a
.TEXCLASS
.ORD
}if(f
===a
.TEXCLASS
.VCENTER
){f
=a
.TEXCLASS
.ORD
}var h
=this.TEXSPACE
[g
][f
];if(this.prevLevel
>0&&this.Get("scriptlevel")>0&&h
>=0){return""}return this.TEXSPACELENGTH
[Math
.abs(h
)]},TEXSPACELENGTH
:["",a
.LENGTH
.THINMATHSPACE
,a
.LENGTH
.MEDIUMMATHSPACE
,a
.LENGTH
.THICKMATHSPACE
],TEXSPACE
:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(f
){return""},isSpacelike:function(){return d
},isEmbellished:function(){return d
},Core:function(){return this},CoreMO:function(){return this},lineBreak:function(){if(this.isEmbellished()){return this.CoreMO().lineBreak()}else{return"none"}},array:function(){if(this.inferred
){return this.data
}else{return[this]}},toString:function(){return this.type
+"("+this.data
.join(",")+")"}},{childrenSpacelike:function(){for(var f
=0;f
<this.data
.length
;f
++){if(!this.data
[f
].isSpacelike()){return d
}}return b
},childEmbellished:function(){return(this.data
[0]&&this.data
[0].isEmbellished())},childCore:function(){return this.data
[0]},childCoreMO:function(){return(this.data
[0]?this.data
[0].CoreMO():null)},setChildTeXclass:function(f
){if(this.data
[0]){f
=this.data
[0].setTeXclass(f
);this.updateTeXclass(this.data
[0])}return f
},setBaseTeXclasses:function(h
){this.getPrevClass(h
);this.texClass
=null;if(this.isEmbellished()){h
=this.data
[0].setTeXclass(h
);this.updateTeXclass(this.Core())}else{if(this.data
[0]){this.data
[0].setTeXclass()}h
=this}for(var g
=1,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]){this.data
[g
].setTeXclass()}}return h
},setSeparateTeXclasses:function(h
){this.getPrevClass(h
);for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]){this.data
[g
].setTeXclass()}}if(this.isEmbellished()){this.updateTeXclass(this.Core())}return this}});a
.mi
=a
.mbase
.Subclass({type
:"mi",isToken
:b
,texClass
:a
.TEXCLASS
.ORD
,defaults
:{mathvariant
:a
.AUTO
,mathsize
:a
.INHERIT
,mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
},autoDefault:function(g
){if(g
==="mathvariant"){var f
=(this.data
[0]||"").toString();return(f
.length
===1||(f
.length
===2&&f
.charCodeAt(0)===this.PLANE1
)?a
.VARIANT
.ITALIC
:a
.VARIANT
.NORMAL
)}return""}});a
.mn
=a
.mbase
.Subclass({type
:"mn",isToken
:b
,texClass
:a
.TEXCLASS
.ORD
,defaults
:{mathvariant
:a
.INHERIT
,mathsize
:a
.INHERIT
,mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
}});a
.mo
=a
.mbase
.Subclass({type
:"mo",isToken
:b
,defaults
:{mathvariant
:a
.INHERIT
,mathsize
:a
.INHERIT
,mathbackground
:a
.INHERIT
,mathcolor
: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
:d
,separator
:d
,lspace
:a
.LENGTH
.THICKMATHSPACE
,rspace
:a
.LENGTH
.THICKMATHSPACE
,stretchy
:d
,symmetric
:b
,maxsize
:a
.SIZE
.INFINITY
,minsize
:"0em",largeop
:d
,movablelimits
:d
,accent
:d
,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,form
:4},useMMLspacing
:7,autoDefault:function(h
,o
){var n
=this.def
;if(!n
){if(h
==="form"){this.useMMLspacing
&=~this.SPACE_ATTR
.form
;return this.getForm()}var l
=this.data
.join("");var g
=[this.Get("form"),a
.FORM
.INFIX
,a
.FORM
.POSTFIX
,a
.FORM
.PREFIX
];for(var j
=0,f
=g
.length
;j
<f
;j
++){var k
=this.OPTABLE
[g
[j
]][l
];if(k
){n
=this.makeDef(k
);break}}if(!n
){n
=this.CheckRange(l
)}if(!n
&&o
){n
={}}else{if(!n
){n
=MathJax
.Hub
.Insert({},this.defaultDef
)}n
.form
=g
[0];this.def
=n
}}this.useMMLspacing
&=~(this.SPACE_ATTR
[h
]||0);if(n
[h
]!=null){return n
[h
]}else{if(!o
){return this.defaultDef
[h
]}}return""},CheckRange:function(k
){var l
=k
.charCodeAt(0);if(k
.charAt(0)===a
.PLANE1
){l
=k
.charCodeAt(1)+119808-56320}for(var h
=0,f
=this.RANGES
.length
;h
<f
&&this.RANGES
[h
][0]<=l
;h
++){if(l
<=this.RANGES
[h
][1]){if(this.RANGES
[h
][3]){var g
=a
.optableDir
+"/"+this.RANGES
[h
][3]+".js";this.RANGES
[h
][3]=null;MathJax
.Hub
.RestartAfter(MathJax
.Ajax
.Require(g
))}var j
=(["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER"])[this.RANGES
[h
][2]];j
=this.OPTABLE
.infix
[k
]=a
.mo
.OPTYPES
[j
==="BIN"?"BIN3":j
];return this.makeDef(j
)}}return null},makeDef:function(g
){if(g
[2]==null){g
[2]=this.defaultDef
.texClass
}if(!g
[3]){g
[3]={}}var f
=MathJax
.Hub
.Insert({},g
[3]);f
.lspace
=this.SPACE
[g
[0]];f
.rspace
=this.SPACE
[g
[1]];f
.texClass
=g
[2];return f
},getForm:function(){var f
=this,h
=this.parent
,g
=this.Parent();while(g
&&g
.isEmbellished()){f
=h
;h
=g
.parent
;g
=g
.Parent()}if(h
&&h
.type
==="mrow"&&h
.NonSpaceLength()!==1){if(h
.FirstNonSpace()===f
){return a
.FORM
.PREFIX
}if(h
.LastNonSpace()===f
){return a
.FORM
.POSTFIX
}}return a
.FORM
.INFIX
},isEmbellished:function(){return b
},lineBreak:function(){var f
=this.getValues("linebreak","linebreakstyle");if(f
.linebreak
===a
.LINEBREAK
.NEWLINE
){if(f
.linebreakstyle
===a
.LINEBREAKSTYLE
.INFIXLINEBREAKSTYLE
){f
.linebreakstyle
=this.Get("infixlinebreakstyle")}return f
.linebreakstyle
}return"none"},setTeXclass:function(f
){this.getValues("lspace","rspace");if(this.useMMLspacing
){this.texClass
=a
.TEXCLASS
.NONE
;return this}this.texClass
=this.Get("texClass");if(f
){this.prevClass
=f
.texClass
||a
.TEXCLASS
.ORD
;this.prevLevel
=f
.Get("scriptlevel")}else{this.prevClass
=a
.TEXCLASS
.NONE
}if(this.texClass
===a
.TEXCLASS
.BIN
&&(this.prevClass
===a
.TEXCLASS
.NONE
||this.prevClass
===a
.TEXCLASS
.BIN
||this.prevClass
===a
.TEXCLASS
.OP
||this.prevClass
===a
.TEXCLASS
.REL
||this.prevClass
===a
.TEXCLASS
.OPEN
||this.prevClass
===a
.TEXCLASS
.PUNCT
)){this.texClass
=a
.TEXCLASS
.ORD
}else{if(this.prevClass
===a
.TEXCLASS
.BIN
&&(this.texClass
===a
.TEXCLASS
.REL
||this.texClass
===a
.TEXCLASS
.CLOSE
||this.texClass
===a
.TEXCLASS
.PUNCT
)){f
.texClass
=this.prevClass
=a
.TEXCLASS
.ORD
}}return this}});a
.mtext
=a
.mbase
.Subclass({type
:"mtext",isToken
:b
,isSpacelike:function(){return b
},texClass
:a
.TEXCLASS
.ORD
,defaults
:{mathvariant
:a
.INHERIT
,mathsize
:a
.INHERIT
,mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
}});a
.mspace
=a
.mbase
.Subclass({type
:"mspace",isToken
:b
,isSpacelike:function(){return b
},defaults
:{mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
,width
:"0em",height
:"0ex",depth
:"0ex",linebreak
:a
.LINEBREAK
.AUTO
},lineBreak:function(){return(this.Get("linebreak")===a
.LINEBREAK
.NEWLINE
?a
.LINEBREAKSTYLE
.AFTER
:"none")}});a
.ms
=a
.mbase
.Subclass({type
:"ms",isToken
:b
,texClass
:a
.TEXCLASS
.ORD
,defaults
:{mathvariant
:a
.INHERIT
,mathsize
:a
.INHERIT
,mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
,lquote
:'"',rquote
:'"'}});a
.mglyph
=a
.mbase
.Subclass({type
:"mglyph",isToken
:b
,texClass
:a
.TEXCLASS
.ORD
,defaults
:{mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
,alt
:"",src
:"",width
:a
.AUTO
,height
:a
.AUTO
,valign
:"0em"}});a
.mrow
=a
.mbase
.Subclass({type
:"mrow",isSpacelike
:a
.mbase
.childrenSpacelike
,inferred
:d
,isEmbellished:function(){var g
=d
;for(var h
=0,f
=this.data
.length
;h
<f
;h
++){if(this.data
[h
]==null){continue}if(this.data
[h
].isEmbellished()){if(g
){return d
}g
=b
;this.core
=h
}else{if(!this.data
[h
].isSpacelike()){return d
}}}return g
},NonSpaceLength:function(){var h
=0;for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]&&!this.data
[g
].isSpacelike()){h
++}}return h
},FirstNonSpace:function(){for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]&&!this.data
[g
].isSpacelike()){return this.data
[g
]}}return null},LastNonSpace:function(){for(var f
=this.data
.length
-1;f
>=0;f
--){if(this.data
[0]&&!this.data
[f
].isSpacelike()){return this.data
[f
]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core
)==="undefined"){return this}return this.data
[this.core
]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core
)==="undefined"){return this}return this.data
[this.core
].CoreMO()},toString:function(){if(this.inferred
){return"["+this.data
.join(",")+"]"}return this.SUPER(arguments
).toString
.call(this)},setTeXclass:function(h
){for(var g
=0,f
=this.data
.length
;g
<f
;g
++){if(this.data
[g
]){h
=this.data
[g
].setTeXclass(h
)}}if(this.data
[0]){this.updateTeXclass(this.data
[0])}return h
}});a
.mfrac
=a
.mbase
.Subclass({type
:"mfrac",num
:0,den
:1,texClass
:a
.TEXCLASS
.INNER
,isEmbellished
:a
.mbase
.childEmbellished
,Core
:a
.mbase
.childCore
,CoreMO
:a
.mbase
.childCoreMO
,defaults
:{mathbackground
:a
.INHERIT
,mathcolor
:a
.INHERIT
,linethickness
:a
.LINETHICKNESS
.MEDIUM
,numalign
:a
.ALIGN
.CENTER
,denomalign
:a
.ALIGN
.CENTER
,bevelled
:d
},adjustChild_displaystyle:function(f
){return d
},adjustChild_scriptlevel:function(g
){var f
=this.Get("scriptlevel");if(!this.Get("displaystyle")||f
>0){f
++}return f
},adjustChild_texprimestyle:function(f
){if(f
==this.den
){return true}return this.Get("texprimestyle")},setTeXclass
:a
.mbase
.setSeparateTeXclasses
});a
.msqrt
=a
.mbase
.Subclass({type
:"msqrt",inferRow
:b
,texClass
:a
.TEXCLASS
.ORD
,setTeXclass
:a
.mbase
.setSeparateTeXclasses
,adjustChild_texprimestyle:function(f
){return b
}});a
.mroot
=a
.mbase
.Subclass({type
:"mroot",texClass
:a
.TEXCLASS
.ORD
,adjustChild_displaystyle:function(f
){if(f
===1){return d
}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g
){var f
=this.Get("scriptlevel");if(g
===1){f
+=2}return f
},adjustChild_texprimestyle:function(f
){if(f
===0){return b
}return this.Get("texprimestyle")},setTeXclass
:a
.mbase
.setSeparateTeXclasses
});a
.mstyle
=a
.mbase
.Subclass({type
:"mstyle",isSpacelike
:a
.mbase
.childrenSpacelike
,isEmbellished
:a
.mbase
.childEmbellished
,Core
:a
.mbase
.childCore
,CoreMO
:a
.mbase
.childCoreMO
,inferRow
:b
,defaults
:{scriptlevel
:a
.INHERIT
,displaystyle
:a
.INHERIT
,scriptsizemultiplier
:Math
.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(h){var g=this.scriptlevel;if(g==null){g=this.Get("scriptlevel")}else{if(String(g).match(/^ *[-+]/)){delete this.scriptlevel;var f=this.Get("scriptlevel");this.scriptlevel=g;g=f+parseInt(g)}}return g},inheritFromMe:b,noInherit:{mpadded:{width:b,height:b,depth:b,lspace:b,voffset:b},mtable:{width:b,height:b,depth:b,align:b}},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:b,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:b,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},texClass:a.TEXCLASS.OPEN,setTeXclass:function(j){this.getPrevClass(j);var g=this.getValues("open","close","separators");g.open=g.open.replace(/[ \t\n\r]/g,"");g.close=g.close.replace(/[ \t\n\r]/g,"");g.separators=g.separators.replace(/[ \t\n\r]/g,"");if(g.open!==""){this.SetData("open",a.mo(g.open).With({stretchy:true,texClass:a.TEXCLASS.OPEN}));j=this.data.open.setTeXclass(j)}if(g.separators!==""){while(g.separators.length<this.data.length){g.separators+=g.separators.charAt(g.separators.length-1)}}if(this.data[0]){j=this.data[0].setTeXclass(j)}for(var h=1,f=this.data.length;h<f;h++){if(this.data[h]){if(g.separators!==""){this.SetData("sep"+h,a.mo(g.separators.charAt(h-1)));j=this.data["sep"+h].setTeXclass(j)}j=this.data[h].setTeXclass(j)}}if(g.close!==""){this.SetData("close",a.mo(g.close).With({stretchy:true,texClass:a.TEXCLASS.CLOSE}));j=this.data.close.setTeXclass(j)}this.updateTeXclass(this.data.open);return j}});a.menclose=a.mbase.Subclass({type:"menclose",inferRow:b,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,notation:a.NOTATION.LONGDIV,texClass:a.TEXCLASS.ORD},setTeXclass:a.mbase.setSeparateTeXclasses});a.msubsup=a.mbase.Subclass({type:"msubsup",base:0,sub:1,sup:2,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,subscriptshift:"",superscriptshift:"",texClass:a.AUTO},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}return 0},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g>0){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.sub){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(f){if(f%2===1){return b}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(f){if(f==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(f):a.TEXCLASS.ORD)}if(f==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(f==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return d},adjustChild_displaystyle:function(f){if(f>0){return d}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");if(g==this.under&&!this.Get("accentunder")){f++}if(g==this.over&&!this.Get("accent")){f++}return f},adjustChild_texprimestyle:function(f){if(f===this.base&&this.data[this.over]){return b}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:b,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:d,equalcolumns:d,displaystyle:d,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},inheritFromMe:b,noInherit:{mtable:{align:b,rowalign:b,columnalign:b,groupalign:b,alignmentscope:b,columnwidth:b,width:b,rowspacing:b,columnspacing:b,rowlines:b,columnlines:b,frame:b,framespacing:b,equalrows:b,equalcolumns:b,side:b,minlabelspacing:b,texClass:b,useHeight:1}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!((arguments[g] instanceof a.mtr)||(arguments[g] instanceof a.mlabeledtr))){arguments[g]=a.mtd(arguments[g])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtr=a.mbase.Subclass({type:"mtr",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:b,noInherit:{mrow:{rowalign:b,columnalign:b,groupalign:b},mtable:{rowalign:b,columnalign:b,groupalign:b}},Append:function(){for(var g=0,f=arguments.length;g<f;g++){if(!(arguments[g] instanceof a.mtd)){arguments[g]=a.mtd(arguments[g])}}this.SUPER(arguments).Append.apply(this,arguments)},setTeXclass:a.mbase.setSeparateTeXclasses});a.mtd=a.mbase.Subclass({type:"mtd",inferRow:b,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,rowspan:1,columnspan:1,rowalign:a.INHERIT,columnalign:a.INHERIT,groupalign:a.INHERIT},setTeXclass:a.mbase.setSeparateTeXclasses});a.maligngroup=a.mbase.Subclass({type:"malign",isSpacelike:function(){return b},defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,groupalign:a.INHERIT},inheritFromMe:b,noInherit:{mrow:{groupalign:b},mtable:{groupalign:b}}});a.malignmark=a.mbase.Subclass({type:"malignmark",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,edge:a.SIDE.LEFT},isSpacelike:function(){return b}});a.mlabeledtr=a.mtr.Subclass({type:"mlabeledtr"});a.maction=a.mbase.Subclass({type:"maction",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,actiontype:a.ACTIONTYPE.TOGGLE,selection:1},selected:function(){return this.data[this.Get("selection")-1]||a.NULL},isEmbellished:function(){return this.selected().isEmbellished()},isSpacelike:function(){return this.selected().isSpacelike()},Core:function(){return this.selected().Core()},CoreMO:function(){return this.selected().CoreMO()},setTeXclass:function(f){return this.selected().setTeXclass(f)}});a.semantics=a.mbase.Subclass({type:"semantics",isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{definitionURL:null,encoding:null},setTeXclass:a.mbase.setChildTeXclass});a.annotation=a.mbase.Subclass({type:"annotation",isToken:b,defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a["annotation-xml"]=a.mbase.Subclass({type:"annotation-xml",defaults:{definitionURL:null,encoding:null,cd:"mathmlkeys",name:"",src:null}});a.math=a.mstyle.Subclass({type:"math",defaults:{mathvariant:a.VARIANT.NORMAL,mathsize:a.SIZE.NORMAL,mathcolor:"",mathbackground:a.COLOR.TRANSPARENT,scriptlevel:0,displaystyle:a.AUTO,display:"inline",maxwidth:"",overflow:a.OVERFLOW.LINEBREAK,altimg:"","altimg-width":"","altimg-height":"","altimg-valign":"",alttext:"",cdgroup:"",scriptsizemultiplier:Math.sqrt(1/2),scriptminsize
:"8px",infixlinebreakstyle
:a
.LINEBREAKSTYLE
.BEFORE
,lineleading
:"1ex",indentshift
:"auto",indentalign
:a
.INDENTALIGN
.AUTO
,indentalignfirst
:a
.INDENTALIGN
.INDENTALIGN
,indentshiftfirst
:a
.INDENTSHIFT
.INDENTSHIFT
,decimalseparator
:".",texprimestyle
:d
},autoDefault:function(f
){if(f
==="displaystyle"){return this.Get("display")==="block"}return""},setTeXclass
:a
.mbase
.setChildTeXclass
});a
.chars
=a
.mbase
.Subclass({type
:"chars",Append:function(){this.data
.push
.apply(this.data
,arguments
)},value:function(){return this.data
.join("")},toString:function(){return this.data
.join("")}});a
.entity
=a
.mbase
.Subclass({type
:"entity",Append:function(){this.data
.push
.apply(this.data
,arguments
)},value:function(){if(this.data
[0].substr(0,2)==="#x"){return parseInt(this.data
[0].substr(2),16)}else{if(this.data
[0].substr(0,1)==="#"){return parseInt(this.data
[0].substr(1))}else{return 0}}},toString:function(){var f
=this.value();if(f
<=65535){return String
.fromCharCode(f
)}return this.PLANE1
+String
.fromCharCode(f
-119808+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 g
=0,f
=arguments
.length
;g
<f
;g
++){var h
=this.Import(arguments
[g
]);this.data
.push(h
);this.div
.appendChild(h
)}},Import:function(k
){if(document
.importNode
){return document
.importNode(k
,true)}var g
,h
,f
;if(k
.nodeType
===1){g
=document
.createElement(k
.nodeName
);if(k
.className
){g
.className
=iNode
.className
}for(h
=0,f
=k
.attributes
.length
;h
<f
;h
++){var j
=k
.attributes
[h
];if(j
.specified
&&j
.nodeValue
!=null&&j
.nodeValue
!=""){g
.setAttribute(j
.nodeName
,j
.nodeValue
)}if(j
.nodeName
==="style"){g
.style
.cssText
=j
.nodeValue
}}if(k
.className
){g
.className
=k
.className
}}else{if(k
.nodeType
===3||k
.nodeType
===4){g
=document
.createTextNode(k
.nodeValue
)}else{if(k
.nodeType
===8){g
=document
.createComment(k
.nodeValue
)}else{return document
.createTextNode("")}}}for(h
=0,f
=k
.childNodes
.length
;h
<f
;h
++){g
.appendChild(this.Import(k
.childNodes
[h
]))}return g
},value:function(){return this.div
},toString:function(){return this.div
.innerHTML
}});a
.TeXAtom
=a
.mbase
.Subclass({type
:"texatom",inferRow
:b
,texClass
:a
.TEXCLASS
.ORD
,setTeXclass:function(f
){this.getPrevClass(f
);this.data
[0].setTeXclass();return this}});a
.NULL
=a
.mbase().With({type
:"null"});var c
=a
.TEXCLASS
;var e
={ORD
:[0,0,c
.ORD
],ORD11
:[1,1,c
.ORD
],ORD21
:[2,1,c
.ORD
],ORD02
:[0,2,c
.ORD
],ORD55
:[5,5,c
.ORD
],OP
:[1,2,c
.OP
,{largeop
:true,movablelimits
:true,symmetric
:true}],OPFIXED
:[1,2,c
.OP
,{largeop
:true,movablelimits
:true}],INTEGRAL
:[0,1,c
.OP
,{largeop
:true,symmetric
:true}],INTEGRAL2
:[1,2,c
.OP
,{largeop
:true,symmetric
:true}],BIN3
:[3,3,c
.BIN
],BIN4
:[4,4,c
.BIN
],BIN01
:[0,1,c
.BIN
],TALLBIN
:[4,4,c
.BIN
,{stretchy
:true}],BINOP
:[4,4,c
.BIN
,{largeop
:true,movablelimits
:true}],REL
:[5,5,c
.REL
],REL1
:[1,1,c
.REL
,{stretchy
:true}],REL4
:[4,4,c
.REL
],WIDEREL
:[5,5,c
.REL
,{stretchy
:true}],RELACCENT
:[5,5,c
.REL
,{accent
:true,stretchy
:true}],OPEN
:[0,0,c
.OPEN
,{fence
:true,stretchy
:true,symmetric
:true}],CLOSE
:[0,0,c
.CLOSE
,{fence
:true,stretchy
:true,symmetric
:true}],INNER
:[0,0,c
.INNER
],PUNCT
:[0,3,c
.PUNCT
],ACCENT
:[0,0,c
.ORD
,{accent
:true}],WIDEACCENT
:[0,0,c
.ORD
,{accent
:true,stretchy
:true}]};a
.mo
.Augment({SPACE
:["0em","0.1111em","0.1667em","0.2222em","0.2667em","0.3333em"],RANGES
:[[32,127,c
.REL
,"BasicLatin"],[160,255,c
.ORD
,"Latin1Supplement"],[256,383,c
.ORD
],[384,591,c
.ORD
],[688,767,c
.ORD
,"SpacingModLetters"],[768,879,c
.ORD
,"CombDiacritMarks"],[880,1023,c
.ORD
,"GreekAndCoptic"],[7680,7935,c
.ORD
],[8192,8303,c
.PUNCT
,"GeneralPunctuation"],[8304,8351,c
.ORD
],[8352,8399,c
.ORD
],[8400,8447,c
.ORD
,"CombDiactForSymbols"],[8448,8527,c
.ORD
,"LetterlikeSymbols"],[8528,8591,c
.ORD
],[8592,8703,c
.REL
,"Arrows"],[8704,8959,c
.BIN
,"MathOperators"],[8960,9215,c
.ORD
,"MiscTechnical"],[9312,9471,c
.ORD
],[9632,9727,c
.ORD
,"GeometricShapes"],[9984,10175,c
.ORD
,"Dingbats"],[10176,10223,c
.ORD
,"MiscMathSymbolsA"],[10496,10623,c
.REL
,"SupplementalArrowsB"],[10624,10751,c
.ORD
,"MiscMathSymbolsB"],[10752,11007,c
.BIN
,"SuppMathOperators"],[11008,11263,c
.ORD
],[119808,120831,c
.ORD
]],OPTABLE
:{prefix
:{"\u2111":e
.ORD11
,"\u2113":e
.ORD11
,"\u211C":e
.ORD11
,"\u2200":e
.ORD21
,"\u2202":e
.ORD21
,"\u2203":e
.ORD21
,"\u2207":e
.ORD21
,"\u220F":e
.OP
,"\u2210":e
.OP
,"\u2211":e
.OP
,"\u2212":e
.BIN01
,"\u2213":e
.BIN01
,"\u221A":[1,1,c
.ORD
,{stretchy
:true}],"\u2220":e
.ORD
,"\u222B":e
.INTEGRAL
,"\u222E":e
.INTEGRAL
,"\u22C0":e
.OP
,"\u22C1":e
.OP
,"\u22C2":e
.OP
,"\u22C3":e
.OP
,"\u2308":e
.OPEN
,"\u230A":e
.OPEN
,"\u27E8":e
.OPEN
,"\u2A00":e
.OP
,"\u2A01":e
.OP
,"\u2A02":e
.OP
,"\u2A04":e
.OP
,"\u2A06":e
.OP
,"\u00AC":e
.ORD21
,"\u00B1":e
.BIN01
,"(":e
.OPEN
,"+":e
.BIN01
,"-":e
.BIN01
,"[":e
.OPEN
,"{":e
.OPEN
,"|":e
.OPEN
},postfix
:{"!":[1,0,c
.CLOSE
],"&":e
.ORD
,"\u2032":e
.ORD02
,"\u203E":e
.WIDEACCENT
,"\u2309":e
.CLOSE
,"\u230B":e
.CLOSE
,"\u23DE":e
.WIDEACCENT
,"\u23DF":e
.WIDEACCENT
,"\u266D":e
.ORD02
,"\u266E":e
.ORD02
,"\u266F":e
.ORD02
,"\u27E9":e
.CLOSE
,"\u02C6":e
.WIDEACCENT
,"\u02C7":e
.WIDEACCENT
,"\u02D8":e
.ACCENT
,"\u02D9":e
.ACCENT
,"\u02DC":e
.WIDEACCENT
,"\u0302":e
.ACCENT
,"\u00A8":e
.ACCENT
,"\u00AF":e
.WIDEACCENT
,")":e
.CLOSE
,"]":e
.CLOSE
,"^":e
.WIDEACCENT
,_
:e
.WIDEACCENT
,"`":e
.ACCENT
,"|":e
.CLOSE
,"}":e
.CLOSE
,"~":e
.WIDEACCENT
},infix
:{"%":[3,3,c
.ORD
],"\u2022":e
.BIN4
,"\u2026":e
.INNER
,"\u2044":e
.TALLBIN
,"\u2061":e
.ORD
,"\u2062":e
.ORD
,"\u2063":[0,0,c
.ORD
,{separator
:true}],"\u2064":e
.ORD
,"\u2190":e
.RELACCENT
,"\u2191":e
.WIDEREL
,"\u2192":e
.RELACCENT
,"\u2193":e
.WIDEREL
,"\u2194":e
.RELACCENT
,"\u2195":e
.WIDEREL
,"\u2196":e
.WIDEREL
,"\u2197":e
.WIDEREL
,"\u2198":e
.WIDEREL
,"\u2199":e
.WIDEREL
,"\u21A6":e
.WIDEREL
,"\u21A9":e
.WIDEREL
,"\u21AA":e
.WIDEREL
,"\u21BC":e
.RELACCENT
,"\u21BD":e
.WIDEREL
,"\u21C0":e
.RELACCENT
,"\u21C1":e
.WIDEREL
,"\u21CC":e
.WIDEREL
,"\u21D0":e
.WIDEREL
,"\u21D1":e
.WIDEREL
,"\u21D2":e
.WIDEREL
,"\u21D3":e
.WIDEREL
,"\u21D4":e
.WIDEREL
,"\u21D5":e
.WIDEREL
,"\u2208":e
.REL
,"\u2209":e
.REL
,"\u220B":e
.REL
,"\u2212":e
.BIN4
,"\u2213":e
.BIN4
,"\u2215":e
.TALLBIN
,"\u2216":e
.BIN4
,"\u2217":e
.BIN4
,"\u2218":e
.BIN4
,"\u2219":e
.BIN4
,"\u221D":e
.REL
,"\u2223":e
.REL
,"\u2225":e
.REL
,"\u2227":e
.BIN4
,"\u2228":e
.BIN4
,"\u2229":e
.BIN4
,"\u222A":e
.BIN4
,"\u223C":e
.REL
,"\u2240":e
.BIN4
,"\u2243":e
.REL
,"\u2245":e
.REL
,"\u2248":e
.REL
,"\u224D":e
.REL
,"\u2250":e
.REL
,"\u2260":e
.REL
,"\u2261":e
.REL
,"\u2264":e
.REL
,"\u2265":e
.REL
,"\u226A":e
.REL
,"\u226B":e
.REL
,"\u227A":e
.REL
,"\u227B":e
.REL
,"\u2282":e
.REL
,"\u2283":e
.REL
,"\u2286":e
.REL
,"\u2287":e
.REL
,"\u228E":e
.BIN4
,"\u2291":e
.REL
,"\u2292":e
.REL
,"\u2293":e
.BIN4
,"\u2294":e
.BIN4
,"\u2295":e
.BIN4
,"\u2296":e
.BIN4
,"\u2297":e
.BIN4
,"\u2298":e
.BIN4
,"\u2299":e
.BIN4
,"\u22A2":e
.REL
,"\u22A3":e
.REL
,"\u22A4":e
.ORD55
,"\u22A5":e
.REL
,"\u22A8":e
.REL
,"\u22C4":e
.BIN4
,"\u22C5":e
.BIN4
,"\u22C6":e
.BIN4
,"\u22C8":e
.REL
,"\u22EE":e
.ORD55
,"\u22EF":e
.INNER
,"\u22F1":[5,5,c
.INNER
],"\u2500":[0,0,c
.ORD
,{stretchy
:true}],"\u25B3":e
.BIN4
,"\u25B5":e
.BIN4
,"\u25B9":e
.BIN4
,"\u25BD":e
.BIN4
,"\u25BF":e
.BIN4
,"\u25C3":e
.BIN4
,"\u2758":[4,4,c
.REL
,{fence
:true,stretchy
:true,symmetric
:true}],"\u27F5":e
.REL1
,"\u27F6":e
.REL1
,"\u27F7":e
.REL1
,"\u27F8":e
.REL1
,"\u27F9":e
.REL1
,"\u27FA":e
.REL1
,"\u2A2F":e
.BIN4
,"\u2A3F":e
.BIN4
,"\u2AAF":e
.REL
,"\u2AB0":e
.REL
,"\u00B1":e
.BIN4
,"\u00B7":e
.BIN4
,"\u00D7":e
.BIN4
,"\u00F7":e
.BIN4
,"*":e
.BIN3
,"+":e
.BIN4
,",":[0,3,c
.PUNCT
,{separator
:true}],"-":e
.BIN4
,".":[3,3,c
.ORD
],"/":e
.ORD11
,":":[1,2,c
.REL
],";":[0,3,c
.PUNCT
,{separator
:true}],"<":e
.REL
,"=":e
.REL
,">":e
.REL
,"?":[1,1,c
.CLOSE
],"\\":e
.ORD
,_
:e
.ORD11
,"|":[2,2,c
.ORD
,{fence
:true,stretchy
:true,symmetric
:true}],"#":e
.ORD
,"$":e
.ORD
,"\u002E":[0,3,c
.PUNCT
,{separator
:true}],"\u02B9":e
.ORD
,"\u02C9":e
.ACCENT
,"\u02CA":e
.ACCENT
,"\u02CB":e
.ACCENT
,"\u0300":e
.ACCENT
,"\u0301":e
.ACCENT
,"\u0303":e
.WIDEACCENT
,"\u0304":e
.ACCENT
,"\u0306":e
.ACCENT
,"\u0307":e
.ACCENT
,"\u0308":e
.ACCENT
,"\u030C":e
.ACCENT
,"\u0332":e
.WIDEACCENT
,"\u0338":e
.REL4
,"\u2015":[0,0,c
.ORD
,{stretchy
:true}],"\u2017":[0,0,c
.ORD
,{stretchy
:true}],"\u2020":e
.BIN3
,"\u2021":e
.BIN3
,"\u20D7":e
.ACCENT
,"\u2118":e
.ORD
,"\u2205":e
.ORD
,"\u221E":e
.ORD
,"\u2305":e
.BIN3
,"\u2306":e
.BIN3
,"\u2322":e
.REL4
,"\u2323":e
.REL4
,"\u2329":e
.OPEN
,"\u232A":e
.CLOSE
,"\u23AA":e
.ORD
,"\u23AF":[0,0,c
.ORD
,{stretchy
:true}],"\u23B0":e
.OPEN
,"\u23B1":e
.CLOSE
,"\u25EF":e
.BIN3
,"\u2660":e
.ORD
,"\u2661":e
.ORD
,"\u2662":e
.ORD
,"\u2663":e
.ORD
,"\u27EE":e
.OPEN
,"\u27EF":e
.CLOSE
,"\u27FC":e
.REL4
,"\u3008":e
.OPEN
,"\u3009":e
.CLOSE
,"\uFE37":e
.WIDEACCENT
,"\uFE38":e
.WIDEACCENT
}}},{OPTYPES
:e
})})(MathJax
.ElementJax
.mml
);MathJax
.ElementJax
.mml
.loadComplete("jax.js");
44 MathJax
.Hub
.Register
.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var b
="1.1.1";var a
=MathJax
.ElementJax
.mml
;a
.mbase
.Augment({toMathML:function(k
){var g
=(this.inferred
&&this.parent
.inferRow
);if(k
==null){k
=""}var e
=this.type
,d
=this.MathMLattributes();if(e
==="mspace"){return k
+"<"+e
+d
+" />"}var j
=[];var h
=(this.isToken
?"":k
+(g
?"":" "));for(var f
=0,c
=this.data
.length
;f
<c
;f
++){if(this.data
[f
]){j
.push(this.data
[f
].toMathML(h
))}else{if(!this.isToken
){j
.push(h
+"<mrow />")}}}if(this.isToken
){return k
+"<"+e
+d
+">"+j
.join("")+"</"+e
+">"}if(g
){return j
.join("\n")}if(j
.length
===0||(j
.length
===1&&j
[0]==="")){return k
+"<"+e
+d
+" />"}return k
+"<"+e
+d
+">\n"+j
.join("\n")+"\n"+k
+"</"+e
+">"},MathMLattributes:function(){var j
=[],g
=this.defaults
;var c
=this.copyAttributes
,l
=this.skipAttributes
;if(this.type
==="math"){j
.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(this.type
==="mstyle"){g
=a
.math
.prototype.defaults
}for(var d
in g
){if(!l
[d
]&&g
.hasOwnProperty(d
)){var e
=(d
==="open"||d
==="close");if(this[d
]!=null&&(e
||this[d
]!==g
[d
])){var k
=this[d
];delete this[d
];if(e
||this.Get(d
)!==k
){j
.push(d
+'="'+this.quoteHTML(k
)+'"')}this[d
]=k
}}}for(var h
=0,f
=c
.length
;h
<f
;h
++){if(this[c
[h
]]!=null){j
.push(c
[h
]+'="'+this.quoteHTML(this[c
[h
]])+'"')}}if(j
.length
){return" "+j
.join(" ")}else{return""}},copyAttributes
:["fontfamily","fontsize","fontweight","fontstyle","color","background","id","class","href","style"],skipAttributes
:{texClass
:1,useHeight
:1,texprimestyle
:1},quoteHTML:function(e
){e
=String(e
).split("");for(var f
=0,d
=e
.length
;f
<d
;f
++){var h
=e
[f
].charCodeAt(0);if(h
<32||h
>126){e
[f
]="&#x"+h
.toString(16).toUpperCase()+";"}else{var g
={"&":"&","<":"<",">":">",'"':"""}[e
[f
]];if(g
){e
[f
]=g
}}}return e
.join("")}});a
.msubsup
.Augment({toMathML:function(h
){var e
=this.type
;if(this.data
[this.sup
]==null){e
="msub"}if(this.data
[this.sub
]==null){e
="msup"}var d
=this.MathMLattributes();delete this.data
[0].inferred
;var g
=[];for(var f
=0,c
=this.data
.length
;f
<c
;f
++){if(this.data
[f
]){g
.push(this.data
[f
].toMathML(h
+" "))}}return h
+"<"+e
+d
+">\n"+g
.join("\n")+"\n"+h
+"</"+e
+">"}});a
.munderover
.Augment({toMathML:function(h
){var e
=this.type
;if(this.data
[this.under
]==null){e
="mover"}if(this.data
[this.over
]==null){e
="munder"}var d
=this.MathMLattributes();delete this.data
[0].inferred
;var g
=[];for(var f
=0,c
=this.data
.length
;f
<c
;f
++){if(this.data
[f
]){g
.push(this.data
[f
].toMathML(h
+" "))}}return h
+"<"+e
+d
+">\n"+g
.join("\n")+"\n"+h
+"</"+e
+">"}});a
.TeXAtom
.Augment({toMathML:function(c
){return c
+"<mrow>\n"+this.data
[0].toMathML(c
+" ")+"\n"+c
+"</mrow>"}});a
.chars
.Augment({toMathML:function(c
){return(c
||"")+this.quoteHTML(this.toString())}});a
.entity
.Augment({toMathML:function(c
){return(c
||"")+"&"+this.data
[0]+";<!-- "+this.toString()+" -->"}});a
.xml
.Augment({toMathML:function(c
){return(c
||"")+this.toString()}});MathJax
.Hub
.Register
.StartupHook("TeX mathchoice Ready",function(){a
.TeXmathchoice
.Augment({toMathML:function(c
){return this.Core().toMathML(c
)}})});MathJax
.Hub
.Startup
.signal
.Post("toMathML Ready")});MathJax
.Ajax
.loadComplete("[MathJax]/extensions/toMathML.js");
46 (function(){var c
="1.1";var a
=MathJax
.Hub
.CombineConfig("TeX.noErrors",{multiLine
:true,inlineDelimiters
:["",""],style
:{"font-family":"serif","font-size":"80%","text-align":"left",color
:"black",padding
:"1px 3px",border
:"1px solid"}});var b
="\u00A0";MathJax
.Extension
["TeX/noErrors"]={version
:c
,config
:a
};MathJax
.Hub
.Register
.StartupHook("TeX Jax Ready",function(){MathJax
.InputJax
.TeX
.Augment({formatError:function(f
,e
,g
,d
){var i
=a
.inlineDelimiters
;var h
=(g
||a
.multiLine
);if(!g
){e
=i
[0]+e
+i
[1]}if(h
){e
=e
.replace(/ /g,b)}else{e=e.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(e).With({isError:true,multiLine:h})}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Config",function(){MathJax.Hub.Config({"HTML-CSS":{styles:{".MathJax .merror":MathJax.Hub.Insert({"font-style":null,"background-color":null,"vertical-align":(MathJax.Hub.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})})})();MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var b=MathJax.OutputJax["HTML-CSS"];var c=a.math.prototype.toHTML;a.math.Augment({toHTML:function(d,e){if(this.data[0]&&this.data[0].data[0]&&this.data[0].data[0].isError){return this.data[0].data[0].toHTML(d)}return c.call(this,d,e)}});a.merror.Augment({toHTML:function(j){if(!this.isError){return a.mbase.prototype.toHTML.call(this,j)}j=this.HTMLcreateSpan(j);if(this.multiLine){j.style.display="inline-block"}var l=this.data[0].data[0].data.join("").split(/\n/);for(var g=0,e=l.length;g<e;g++){b.addText(j,l[g]);if(g!==e-1){b.addElement(j,"br")}}var n=b.getHD(j.parentNode),d=b.getW(j.parentNode);if(e>1){var k=(n.h+n.d)/2,h
=b
.TeX
.x_height
/2;var f=b.config.styles[".MathJax .merror"]["font-size"];if(f&&f.match(/%/)){h*=parseInt(f)/100}j
.parentNode
.style
.verticalAlign
=b
.Em(n
.d
+(h
-k
));n
.h
=h
+k
;n
.d
=k
-h
}j
.bbox
={h
:n
.h
,d
:n
.d
,w
:d
,lw
:0,rw
:d
};return j
}});MathJax
.Hub
.Startup
.signal
.Post("TeX noErrors Ready")});MathJax
.Hub
.Register
.StartupHook("NativeMML Jax Ready",function(){var b
=MathJax
.ElementJax
.mml
;var a
=MathJax
.Extension
["TeX/noErrors"].config
;var c
=b
.math
.prototype.toNativeMML
;b
.math
.Augment({toNativeMML:function(d
){if(this.data
[0]&&this.data
[0].data
[0]&&this.data
[0].data
[0].isError
){return this.data
[0].data
[0].toNativeMML(d
)}return c
.call(this,d
)}});b
.merror
.Augment({toNativeMML:function(g
){if(!this.isError
){return b
.mbase
.prototype.toNativeMML
.call(this,g
)}g
=g
.appendChild(document
.createElement("span"));var h
=this.data
[0].data
[0].data
.join("").split(/\n/);for(var f=0,e=h.length;f<e;f++){g.appendChild(document.createTextNode(h[f]));if(f!==e-1){g.appendChild(document.createElement("br"))}}if(this.multiLine){g.style.display="inline-block";if(e>1){g.style.verticalAlign="middle"}}for(var j in a.style){if(a.style.hasOwnProperty(j)){var d=j.replace(/-./g,function(i){return i.charAt(1).toUpperCase()});g.style[d]=a.style[j]}}return g}});MathJax.Hub.Startup.signal.Post("TeX noErrors Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions
/TeX/noErrors
.js
");
48 MathJax.Extension["TeX
/noUndefined"]={version:"1.1",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined
"].config;var a=MathJax.ElementJax.mml;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(c){this.Push(a.mtext(c).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready
")});MathJax.Ajax.loadComplete("[MathJax
]/extensions/TeX
/noUndefined
.js
");
50 (function(d){var c=true,f=false,i,h=String.fromCharCode(160);var e=MathJax.Object.Subclass({Init:function(k){this.global={};this.data=[b.start().With({global:this.global})];if(k){this.data[0].env=k}this.env=this.data[0].env},Push:function(){var l,k,n,o;for(l=0,k=arguments.length;l<k;l++){n=arguments[l];if(n instanceof i.mbase){n=b.mml(n)}n.global=this.global;o=(this.data.length?this.Top().checkItem(n):c);if(o instanceof Array){this.Pop();this.Push.apply(this,o)}else{if(o instanceof b){this.Pop();this.Push(o)}else{if(o){this.data.push(n);if(n.env){for(var p in this.env){if(this.env.hasOwnProperty(p)){n.env[p]=this.env[p]}}this.env=n.env}else{n.env=this.env}}}}}},Pop:function(){var k=this.data.pop();if(!k.isOpen){delete k.env}this.env=(this.data.length?this.Top().env:{});return k},Top:function(k){if(k==null){k=1}if(this.data.length<k){return null}return this.data[this.data.length-k]},Prev:function(k){var l=this.Top();if(k){return l.data[l.data.length-1]}else{return l.Pop()}},toString:function(){return"stack
[\n "+this.data.join("\n ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base
",closeError:"Extra close brace or missing open brace
",rightError:"Missing
\\left or extra
\\right
",Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(k,l){if(k==null){k=c}if(this.data.length===1&&!l){return this.data[0]}return i.mrow.apply(i,this.data).With((k?{inferred:c}:{}))},checkItem:function(k){if(k.type==="over
"&&this.isOpen){k.num=this.mmlData(f);this.data=[]}if(k.type==="cell
"&&this.isOpen){d.Error("Misplaced
"+k.name)}if(k.isClose&&this[k.type+"Error
"]){d.Error(this[k.type+"Error
"])}if(!k.isNotStack){return c}this.Push(k.data[0]);return f},With:function(k){for(var l in k){if(k.hasOwnProperty(l)){this[l]=k[l]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start
",isOpen:c,checkItem:function(k){if(k.type==="stop
"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,k)}});b.stop=b.Subclass({type:"stop
",isClose:c});b.open=b.Subclass({type:"open
",isOpen:c,stopError:"Extra open brace or missing close brace
",checkItem:function(l){if(l.type==="close
"){var k=this.mmlData();return b.mml(i.TeXAtom(k))}return this.SUPER(arguments).checkItem.call(this,l)}});b.close=b.Subclass({type:"close
",isClose:c});b.subsup=b.Subclass({type:"subsup
",stopError:"Missing superscript or subscript argument
",checkItem:function(l){var k=["","subscript
","superscript
"][this.position];if(l.type==="open
"||l.type==="left
"){return c}if(l.type==="mml
"){this.data[0].SetData(this.position,l.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error("Missing open brace
for "+k)}},Pop:function(){}});b.over=b.Subclass({type:"over
",isClose:c,name:"\\over
",checkItem:function(m,k){if(m.type==="over
"){d.Error("Ambiguous
use of "+m.name)}if(m.isClose){var l=i.mfrac(this.num,this.mmlData(f));if(this.thickness!=null){l.linethickness=this.thickness}if(this.open||this.close){l.texClass=i.TEXCLASS.INNER;l.texWithDelims=c;l=i.mfenced(l).With({open:this.open,close:this.close})}return[b.mml(l),m]}return this.SUPER(arguments).checkItem.call(this,m)},toString:function(){return"over
["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left
",isOpen:c,delim:"(",stopError:"Extra
\\left or missing
\\right
",checkItem:function(l){if(l.type==="right
"){var k=i.mfenced(this.data.length===1?this.data[0]:i.mrow.apply(i,this.data));return b.mml(k.With({open:this.delim,close:l.delim}))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right
",isClose:c,delim:")"});b.begin=b.Subclass({type:"begin
",isOpen:c,checkItem:function(k){if(k.type==="end
"){if(k.name!==this.name){d.Error("\\begin
{"+this.name+"} ended
with \\end
{"+k.name+"}")}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(k.type==="stop
"){d.Error("Missing
\\end
{"+this.name+"}")}return this.SUPER(arguments).checkItem.call(this,k)}});b.end=b.Subclass({type:"end
",isClose:c});b.style=b.Subclass({type:"style
",checkItem:function(l){if(!l.isClose){return this.SUPER(arguments).checkItem.call(this,l)}var k=i.mstyle.apply(i,this.data).With(this.styles);return[b.mml(k),l]}});b.position=b.Subclass({type:"position
",checkItem:function(l){if(l.isClose){d.Error("Missing box
for "+this.name)}if(l.isNotStack){var k=l.mmlData();switch(this.move){case"vertical
":k=i.mpadded(k).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(k)];case"horizontal
":return[b.mml(this.left),l,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,l)}});b.array=b.Subclass({type:"array
",isOpen:c,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(l){if(l.isClose&&l.type!=="over
"){if(l.isEntry){this.EndEntry();this.clearEnv();return f}if(l.isCR){this.EndEntry();this.EndRow();this.clearEnv();return f}this.EndTable();this.clearEnv();var k=i.mtable.apply(i,this.table).With(this.arraydef);if(this.open||this.close){k=i.mfenced(k).With({open:this.open,close:this.close})}k=b.mml(k);if(this.requireClose){if(l.type==="close
"){return k}d.Error("Missing close brace
")}return[k,l]}return this.SUPER(arguments).checkItem.call(this,l)},EndEntry:function(){this.row.push(i.mtd.apply(i,this.data));this.data=[]},EndRow:function(){this.table.push(i.mtr.apply(i,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var k=this.arraydef.rowlines.split(/ /);if(k.length===this.table.length){this.arraydef.frame=k.pop();this.arraydef.rowlines=k.join(" ")}else{if(k.length<this.table.length-1){this.arraydef.rowlines+=" none
"}}}},clearEnv:function(){for(var k in this.env){if(this.env.hasOwnProperty(k)){delete this.env[k]}}}});b.cell=b.Subclass({type:"cell
",isClose:c});b.mml=b.Subclass({type:"mml
",isNotStack:c,Push:function(){for(var l=0,k=arguments.length;l<k;l++){if(arguments[l].type!=="mo
"&&arguments[l].isEmbellished()){arguments[l]=i.TeXAtom(arguments[l]).With({isEmbellishedWrapper:c})}}this.data.push.apply(this.data,arguments)},Add:function(){this.data.push.apply(this.data,arguments);return this}});var g={};var j=function(){i=MathJax.ElementJax.mml;MathJax.Hub.Insert(g,{letter:/[a-z]/i,digit:/[0-9.]/,number:/^(?:[0-9]+(?:\{,\}[0-9]{3})*(?:\.[0-9]*)*|\.[0-9]+)/,special:{"\\":"ControlSequence
","{":"Open
","}":"Close
","~":"Tilde
","^":"Superscript
",_:"Subscript
"," ":"Space
","\t":"Space
","\r":"Space
","\n":"Space
","'":"Prime","%":"Comment","&":"Entry","#":"Hash","\u2019":"Prime"},remap:{"-":"2212","*":"2217"},mathchar0mi:{alpha:"03B1",beta:"03B2",gamma:"03B3",delta:"03B4",epsilon:"03F5",zeta:"03B6",eta:"03B7",theta:"03B8",iota:"03B9",kappa:"03BA",lambda:"03BB",mu:"03BC",nu:"03BD",xi:"03BE",omicron:"03BF",pi:"03C0",rho:"03C1",sigma:"03C3",tau:"03C4",upsilon:"03C5",phi:"03D5",chi:"03C7",psi:"03C8",omega:"03C9",varepsilon:"03B5",vartheta:"03D1",varpi:"03D6",varrho:"03F1",varsigma:"03C2",varphi:"03C6",S:"00A7",aleph:["2135",{mathvariant:i.VARIANT.NORMAL}],hbar:"210F",imath:"0131",jmath:"0237",ell:"2113",wp:["2118",{mathvariant:i.VARIANT.NORMAL}],Re:["211C",{mathvariant:i.VARIANT.NORMAL}],Im:["2111",{mathvariant:i.VARIANT.NORMAL}],partial:["2202",{mathvariant:i.VARIANT.NORMAL}],infty:["221E",{mathvariant:i.VARIANT.NORMAL}],prime:["2032",{mathvariant:i.VARIANT.NORMAL}],emptyset:["2205",{mathvariant:i.VARIANT.NORMAL}],nabla:["2207",{mathvariant:i.VARIANT.NORMAL}],top:["22A4",{mathvariant:i.VARIANT.NORMAL}],bot:["22A5",{mathvariant:i.VARIANT.NORMAL}],angle:["2220",{mathvariant:i.VARIANT.NORMAL}],triangle:["25B3",{mathvariant:i.VARIANT.NORMAL}],backslash:["2216",{mathvariant:i.VARIANT.NORMAL}],forall:["2200",{mathvariant:i.VARIANT.NORMAL}],exists:["2203",{mathvariant:i.VARIANT.NORMAL}],neg:["00AC",{mathvariant:i.VARIANT.NORMAL}],lnot:["00AC",{mathvariant:i.VARIANT.NORMAL}],flat:["266D",{mathvariant:i.VARIANT.NORMAL}],natural:["266E",{mathvariant:i.VARIANT.NORMAL}],sharp:["266F",{mathvariant:i.VARIANT.NORMAL}],clubsuit:["2663",{mathvariant:i.VARIANT.NORMAL}],diamondsuit:["2662",{mathvariant:i.VARIANT.NORMAL}],heartsuit:["2661",{mathvariant:i.VARIANT.NORMAL}],spadesuit:["2660",{mathvariant:i.VARIANT.NORMAL}]},mathchar0mo:{surd:"221A",coprod:["2210",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigvee:["22C1",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigwedge:["22C0",{texClass:i.TEXCLASS.OP,movesupsub:c}],biguplus:["2A04",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcap:["22C2",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigcup:["22C3",{texClass:i.TEXCLASS.OP,movesupsub:c}],"int":["222B",{texClass:i.TEXCLASS.OP}],intop:["222B",{texClass:i.TEXCLASS.OP,movesupsub:c,movablelimits:c}],iint:["222C",{texClass:i.TEXCLASS.OP}],iiint:["222D",{texClass:i.TEXCLASS.OP}],prod:["220F",{texClass:i.TEXCLASS.OP,movesupsub:c}],sum:["2211",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigotimes:["2A02",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigoplus:["2A01",{texClass:i.TEXCLASS.OP,movesupsub:c}],bigodot:["2A00",{texClass:i.TEXCLASS.OP,movesupsub:c}],oint:["222E",{texClass:i.TEXCLASS.OP}],bigsqcup:["2A06",{texClass:i.TEXCLASS.OP,movesupsub:c}],smallint:["222B",{largeop:f}],triangleleft:"25C3",triangleright:"25B9",bigtriangleup:"25B3",bigtriangledown:"25BD",wedge:"2227",land:"2227",vee:"2228",lor:"2228",cap:"2229",cup:"222A",ddagger:"2021",dagger:"2020",sqcap:"2293",sqcup:"2294",uplus:"228E",amalg:"2A3F",diamond:"22C4",bullet:"2219",wr:"2240",div:"00F7",odot:["2299",{largeop:f}],oslash:["2298",{largeop:f}],otimes:["2297",{largeop:f}],ominus:["2296",{largeop:f}],oplus:["2295",{largeop:f}],mp:"2213",pm:"00B1",circ:"2218",bigcirc:"25EF",setminus:"2216",cdot:"22C5",ast:"2217",times:"00D7",star:"22C6",propto:"221D",sqsubseteq:"2291",sqsupseteq:"2292",parallel:"2225",mid:"2223",dashv:"22A3",vdash:"22A2",leq:"2264",le:"2264",geq:"2265",ge:"2265",lt:"003C",gt:"003E",succ:"227B",prec:"227A",approx:"2248",succeq:"2AB0",preceq:"2AAF",supset:"2283",subset:"2282",supseteq:"2287",subseteq:"2286","in":"2208",ni:"220B",notin:"2209",owns:"220B",gg:"226B",ll:"226A",sim:"223C",simeq:"2243",perp:"22A5",equiv:"2261",asymp:"224D",smile:"2323",frown:"2322",ne:"2260",neq:"2260",cong:"2245",doteq:"2250",bowtie:"22C8",models:"22A8",notChar:"0338",Leftrightarrow:"21D4",Leftarrow:"21D0",Rightarrow:"21D2",leftrightarrow:"2194",leftarrow:"2190",gets:"2190",rightarrow:"2192",to:"2192",mapsto:"21A6",leftharpoonup:"21BC",leftharpoondown:"21BD",rightharpoonup:"21C0",rightharpoondown:"21C1",nearrow:"2197",searrow:"2198",nwarrow:"2196",swarrow:"2199",rightleftharpoons:"21CC",hookrightarrow:"21AA",hookleftarrow:"21A9",longleftarrow:"27F5",Longleftarrow:"27F8",longrightarrow:"27F6",Longrightarrow:"27F9",Longleftrightarrow:"27FA",longleftrightarrow:"27F7",longmapsto:"27FC",ldots:"2026",cdots:"22EF",vdots:"22EE",ddots:"22F1",dots:"2026",dotsc:"2026",dotsb:"22EF",dotsm:"22EF",dotsi:"22EF",dotso:"2026",ldotp:["002E",{texClass:i.TEXCLASS.PUNCT}],cdotp:["22C5",{texClass:i.TEXCLASS.PUNCT}],colon:["003A",{texClass:i.TEXCLASS.PUNCT}]},mathchar7:{Gamma:"0393",Delta:"0394",Theta:"0398",Lambda:"039B",Xi:"039E",Pi:"03A0",Sigma:"03A3",Upsilon:"03A5",Phi:"03A6",Psi:"03A8",Omega:"03A9",_:"005F","#":"0023","$":"0024","%":"0025","&":"0026",And:"0026"},delimiter:{"(":"(",")":")","[":"[","]":"]","<":"27E8",">":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2225",{texClass:i.TEXCLASS.ORD}],"\\|":["2225",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",c,0],textstyle:["SetStyle","T",f,0],scriptstyle:["SetStyle","S",f,1],scriptscriptstyle:["SetStyle","SS",f,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont",i.VARIANT.ITALIC],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedOp",0],arccos:["NamedOp",0],arctan:["NamedOp",0],arg:["NamedOp",0],cos:["NamedOp",0],cosh:["NamedOp",0],cot:["NamedOp",0],coth:["NamedOp",0],csc:["NamedOp",0],deg:["NamedOp",0],det:"NamedOp",dim:["NamedOp",0],exp:["NamedOp",0],gcd:"NamedOp",hom:["NamedOp",0],inf:"NamedOp",ker:["NamedOp",0],lg:["NamedOp",0],lim:"NamedOp",liminf:["NamedOp",null,"lim inf"],limsup:["NamedOp",null,"lim sup"],ln:["NamedOp",0],log:["NamedOp",0],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedOp",0],sin:["NamedOp",0],sinh:["NamedOp",0],sup:"NamedOp",tan:["NamedOp",0],tanh:["NamedOp",0],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","203E"],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.THINMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","02CA"],grave:["Accent","02CB"],ddot:["Accent","00A8"],tilde:["Accent","02DC"],bar:["Accent","02C9"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","02C6"],vec:["Accent","20D7"],dot:["Accent","02D9"],widetilde:["Accent","02DC",1],widehat:["Accent","02C6",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em"],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"Cr",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],leqalignno:["Matrix",null,null,"right left right",i.LENGTH.THICKMATHSPACE+" 3em",".5em","D"],bmod:["Macro","\\mathbin{\\rm mod}"],pmod:["Macro","\\pod{{\\rm mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}{\\rm mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it{\\text{#1}}}",1],textbf:["Macro","\\mathord{\\bf{\\text{#1}}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"],not:["Macro","\\mathrel{\\rlap{\\kern.5em\\notChar}}"]," ":["Macro","\\text{ }"],space:"Tilde",begin:"Begin",end:"End",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],def:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Macro","",1],nonumber:["Macro",""],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],require:"Require"},environment:{array:["Array"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".1em"],eqnarray:["Array",null,null,null,"rcl",i.LENGTH.THICKMATHSPACE,".5em","D"],"eqnarray*":["Array",null,null,null,"rcl",i.LENGTH.THICKMATHSPACE,".5em","D"],equation:[null,"Equation"],"equation*":[null,"Equation"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var k=this.config.Macros;for(var l in k){if(k.hasOwnProperty(l)){if(typeof(k[l])==="string"){g.macros[l]=["Macro",k[l]]}else{g.macros[l]=["Macro"].concat(k[l])}}}}};var a=MathJax.Object.Subclass({Init:function(l,m){this.string=l;this.i=0;this.macroCount=0;var k;if(m){k={};for(var n in m){if(m.hasOwnProperty(n)){k[n]=m[n]}}}this.stack=d.Stack(k);this.Parse();this.Push(b.stop())},Parse:function(){var k;while(this.i<this.string.length){k=this.string.charAt(this.i++);if(g.special[k]){this[g.special[k]](k)}else{if(g.letter.test(k)){this.Variable(k)}else{if(g.digit.test(k)){this.Number(k)}else{this.Other(k)}}}}},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(k){return k},ControlSequence:function(q){var k=this.GetCS(),p,n;if(g.macros[k]){var m=g.macros[k];if(!(m instanceof Array)){m=[m]}var l=m[0];if(!(l instanceof Function)){l=this[l]}l.apply(this,["\\"+k].concat(m.slice(1)))}else{if(g.mathchar0mi[k]){p=g.mathchar0mi[k];n={mathvariant:i.VARIANT.ITALIC};if(p instanceof Array){n=p[1];p=p[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.mathchar0mo[k]){p=g.mathchar0mo[k];n={stretchy:f};if(p instanceof Array){n=p[1];n.stretchy=f;p=p[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+p)).With(n)))}else{if(g.mathchar7[k]){p=g.mathchar7[k];n={mathvariant:i.VARIANT.NORMAL};if(p instanceof Array){n=p[1];p=p[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+p)).With(n)))}else{if(g.delimiter["\\"+k]!=null){var o=g.delimiter["\\"+k];n={};if(o instanceof Array){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:f,stretchy:f}).With(n)))}else{this.csUndefined("\\"+k)}}}}}},csUndefined:function(k){d.Error("Undefined control sequence "+k)},Variable:function(l){var k={};if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(l)).With(k)))},Number:function(m){var k,l=this.string.slice(this.i-1).match(g.number);if(l){k=i.mn(l[0].replace(/[{}]/g,""));this.i+=l[0].length-1}else{k=i.mo(i.chars(m))}if(this.stack.env.font){k.mathvariant=this.stack.env.font}this.Push(this.mmlToken(k))},Open:function(k){this.Push(b.open())},Close:function(k){this.Push(b.close())},Tilde:function(k){this.Push(i.mtext(i.chars(h)))},Space:function(k){},Superscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sup]){if(!l.data[l.sup].isPrime){d.Error("Double exponent: use braces to clarify")}l=i.msubsup(l,null,null)}k=l.sup}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.over]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.over}else{l=i.msubsup(l,null,null);k=l.sup}}this.Push(b.subsup(l).With({position:k}))},Subscript:function(m){var k,l=this.stack.Prev();if(!l){l=i.mi("")}if(l.isEmbellishedWrapper){l=l.data[0].data[0]}if(l.type==="msubsup"){if(l.data[l.sub]){d.Error("Double subscripts: use braces to clarify")}k=l.sub}else{if(l.movesupsub){if(l.type!=="munderover"||l.data[l.under]){l=i.munderover(l,null,null).With({movesupsub:c})}k=l.under}else{l=i.msubsup(l,null,null);k=l.sub}}this.Push(b.subsup(l).With({position:k}))},PRIME:String.fromCharCode(8242),SMARTQUOTE:String.fromCharCode(8217),Prime:function(m){var l=this.stack.Prev();if(!l){l=i.mi()}if(l.type==="msubsup"&&l.data[l.sup]){d.Error("Prime causes double exponent: use braces to clarify")}var k="";this.i--;do{k+=this.PRIME;this.i++,m=this.GetNext()}while(m==="'"||m===this.SMARTQUOTE);k=this.mmlToken(i.mo(i.chars(k)).With({isPrime:c,variantForm:d.isSTIX}));this.Push(i.msubsup(l,null,k))},Comment:function(k){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(k){d.Error("You can
't use 'macro parameter character
#' in math mode")},Other:function(m){var l={stretchy:false},k;if(this.stack.env.font){l.mathvariant=this.stack.env.font}if(g.remap[m]){m=g.remap[m];if(m instanceof Array){l=m[1];m=m[0]}k=i.mo(i.entity("#x"+m))}else{k=i.mo(m)}if(k.autoDefault("texClass",true)==""){k=i.TeXAtom(k)}this.Push(this.mmlToken(k.With(l)))},SetFont:function(l,k){this.stack.env.font=k},SetStyle:function(l,k,m,n){this.stack.env.style=k;this.stack.env.level=n;this.Push(b.style().With({styles:{displaystyle:m,scriptlevel:n}}))},SetSize:function(k,l){this.stack.env.size=l;this.Push(b.style().With({styles:{mathsize:l+"em"}}))},Color:function(m){var l=this.GetArgument(m);var k=this.stack.env.color;this.stack.env.color=l;var n=this.ParseArg(m);if(k){this.stack.env.color}else{delete this.stack.env.color}this.Push(i.mstyle(n).With({mathcolor:l}))},Spacer:function(k,l){this.Push(i.mspace().With({width:l,mathsize:i.SIZE.NORMAL,scriptlevel:1}))},LeftRight:function(k){this.Push(b[k.substr(1)]().With({delim:this.GetDelimiter(k)}))},NamedOp:function(m,l,o){var n=(l!=null&&l===0?f:c);if(!o){o=m.substr(1)}l=((l||l==null)?c:f);o=o.replace(/ /,String.fromCharCode(8198));var k=i.mo(o).With({movablelimits:l,movesupsub:n,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});k.useMMLspacing&=~k.SPACE_ATTR.form;this.Push(this.mmlToken(k))},Limits:function(l,k){var m=this.stack.Prev("nopop");if(m.texClass!==i.TEXCLASS.OP){d.Error(l+" is allowed only on operators")}m.movesupsub=(k?c:f);m.movablelimits=f},Over:function(m,l,n){var k=b.over().With({name:m});if(l||n){k.open=l;k.close=n}else{if(m.match(/withdelims$/)){k.open=this.GetDelimiter(m);k.close=this.GetDelimiter(m)}}if(m.match(/^\\above/)){k.thickness=this.GetDimen(m)}else{if(m.match(/^\\atop/)||l||n){k.thickness=0}}this.Push(k)},Frac:function(l){var k=this.ParseArg(l);var m=this.ParseArg(l);this.Push(i.mfrac(k,m))},Sqrt:function(l){var m=this.GetBrackets(l),k=this.ParseArg(l);if(m==""){k=i.msqrt.apply(i,k.array())}else{k=i.mroot(k,this.parseRoot(m))}this.Push(k)},Root:function(l){var m=this.GetUpTo(l,"\\of");var k=this.ParseArg(l);this.Push(i.mroot(k,this.parseRoot(m)))},parseRoot:function(p){var l=this.stack.env,k=l.inRoot;l.inRoot=true;var o=d.Parse(p,l);p=o.mml();var m=o.stack.global;if(m.leftRoot||m.upRoot){p=i.mpadded(p);if(m.leftRoot){p.width=m.leftRoot}if(m.upRoot){p.voffset=m.upRoot;p.height=m.upRoot}}l.inRoot=k;return p},MoveRoot:function(k,m){if(!this.stack.env.inRoot){d.Error(k+" can appear only within a root")}if(this.stack.global[m]){d.Error("Multiple use of "+k)}var l=this.GetArgument(k);if(!l.match(/-?[0-9]+/)){d.Error("The argument to "+k+" must be an integer")}l=(l/15)+"em";if(l.substr(0,1)!=="-"){l="+"+l}this.stack.global[m]=l},Accent:function(m,k,p){var o=this.ParseArg(m);var n={accent:true};if(this.stack.env.font){n.mathvariant=this.stack.env.font}var l=this.mmlToken(i.mo(i.entity("#x"+k)).With(n));l.stretchy=(p?c:f);this.Push(i.munderover(o,null,l).With({accent:c}))},UnderOver:function(m,p,k){var o={o:"over",u:"under"}[m.charAt(1)];var n=this.ParseArg(m);if(n.Get("movablelimits")){n.movablelimits=false}var l=i.munderover(n,null,null);if(k){l.movesupsub=c}l.data[l[o]]=this.mmlToken(i.mo(i.entity("#x"+p)).With({stretchy:c,accent:(o=="under")}));this.Push(l)},Overset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,null,m))},Underset:function(k){var m=this.ParseArg(k),l=this.ParseArg(k);this.Push(i.munderover(l,m,null))},TeXAtom:function(n,p){var o={texClass:p},m;if(p==i.TEXCLASS.OP){o.movesupsub=o.movablelimits=c;var k=this.GetArgument(n);var l=k.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(l){m=this.mmlToken(i.mo(l[1]).With({movablelimits:c,movesupsub:c,mathvariant:i.VARIANT.NORMAL,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP}));m.useMMLspacing&=~m.SPACE_ATTR.form}else{m=i.TeXAtom(d.Parse(k,this.stack.env).mml()).With(o)}}else{m=i.TeXAtom(this.ParseArg(n)).With(o)}this.Push(m)},Strut:function(k){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(l,k,m){var n=i.mphantom(this.ParseArg(l));if(k||m){n=i.mpadded(n);if(m){n.height=n.depth=0}if(k){n.width=0}}this.Push(n)},Smash:function(m){var l=this.trimSpaces(this.GetBrackets(m));var k=i.mpadded(this.ParseArg(m));switch(l){case"b":k.depth=0;break;case"t":k.height=0;break;default:k.height=k.depth=0}this.Push(k)},Lap:function(l){var k=i.mpadded(this.ParseArg(l)).With({width:0});if(l==="\\llap"){k.lspace="-1 width"}this.Push(k)},RaiseLower:function(k){var l=this.GetDimen(k);var m=b.position().With({name:k,move:"vertical"});if(l.charAt(0)==="-"){l=l.slice(1);k={raise:"\\lower",lower:"\\raise"}[k.substr(1)]}if(k==="\\lower"){m.dh="-"+l;m.dd="+"+l}else{m.dh="+"+l;m.dd="-"+l}this.Push(m)},MoveLeftRight:function(k){var n=this.GetDimen(k);var m=(n.charAt(0)==="-"?n.slice(1):"-"+n);if(k==="\\moveleft"){var l=n;n=m;m=l}this.Push(b.position().With({name:k,move:"horizontal",left:i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:1}),right:i.mspace().With({width:m,mathsize:i.SIZE.NORMAL,scriptlevel:1})}))},Hskip:function(k){this.Push(i.mspace().With({width:this.GetDimen(k),mathsize:i.SIZE.NORMAL,scriptlevel:0}))},Rule:function(m,o){var k=this.GetDimen(m),n=this.GetDimen(m),q=this.GetDimen(m);var l,p={width:k,height:n,depth:q};if(o!=="blank"){l=i.mpadded(i.mrow()).With(p);if(parseFloat(k)&&parseFloat(n)+parseFloat(q)){l=i.mstyle(l).With({mathbackground:(this.stack.env.color||"black")})}}else{l=i.mspace().With(p)}this.Push(l)},MakeBig:function(k,n,l){l*=g.p_height;l=String(l).replace(/(\.\d\d\d).+/,"$1")+"em";var m=this.GetDelimiter(k);this.Push(i.TeXAtom(i.mo(m).With({minsize:l,maxsize:l,scriptlevel:0,fence:c,stretchy:c,symmetric:c})).With({texClass:n}))},BuildRel:function(k){var l=this.ParseUpTo(k,"\\over");var m=this.ParseArg(k);this.Push(i.TeXAtom(i.munderover(m,null,l)).With({mclass:i.TEXCLASS.REL}))},HBox:function(k,l){this.Push.apply(this,this.InternalMath(this.GetArgument(k),l))},FBox:function(k){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(k))).With({notation:"box"}))},Require:function(k){var l=this.GetArgument(k);this.Extension(null,l)},Extension:function(k,l,m){if(k&&!typeof(k)==="string"){k=k.name}l=d.extensionDir+"/"+l;if(!l.match(/\.js$/)){l+=".js"}if(!MathJax.Ajax.loaded[MathJax.Ajax.fileURL(l)]){if(k!=null){delete g[m||"macros"][k.replace(/^\\/,"")]}MathJax.Hub.RestartAfter(MathJax.Ajax.Require(l))}},Macro:function(l,o,n){if(n){var k=[];for(var m=0;m<n;m++){k.push(this.GetArgument(l))}o=this.SubstituteArgs(k,o)}this.string=this.AddArgs(o,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum macro substitution count exceeded; is there a recursive macro call?")}},Matrix:function(l,n,s,p,q,m,k){var r=this.GetNext();if(r===""){d.Error("Missing argument for "+l)}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var o=b.array().With({requireClose:c,arraydef:{rowspacing:(m||"4pt"),columnspacing:(q||"1em")}});if(n||s){o.open=n;o.close=s}if(k==="D"){o.arraydef.displaystyle=c}if(p!=null){o.arraydef.columnalign=p}this.Push(o)},Entry:function(k){this.Push(b.cell().With({isEntry:c,name:k}))},Cr:function(k){this.Push(b.cell().With({isCR:c,name:k}))},HLine:function(l,m){if(m==null){m="solid"}var n=this.stack.Top();if(n.type!=="array"||n.data.length){d.Error("Misplaced "+l)}if(n.table.length==0){n.arraydef.frame=m}else{var k=(n.arraydef.rowlines?n.arraydef.rowlines.split(/ /):[]);while(k.length<n.table.length){k.push("none")}k[n.table.length-1]=m;n.arraydef.rowlines=k.join(" ")}},Begin:function(l){var m=this.GetArgument(l);if(m.match(/[^a-z*]/i)){d.Error('Invalid environment name
"'+m+'"')}if(!g.environment[m]){d.Error('Unknown environment
"'+m+'"')}if(++this.macroCount>d.config.MAXMACROS){d.Error("MathJax maximum substitution count exceeded; is there a recursive latex environment?")}var n=g.environment[m];if(!(n instanceof Array)){n=[n]}var k=b.begin().With({name:m,end:n[1],parse:this});if(n[0]&&this[n[0]]){k=this[n[0]].apply(this,[k].concat(n.slice(2)))}this.Push(k)},End:function(k){this.Push(b.end().With({name:this.GetArgument(k)}))},Equation:function(k,l){return l},ExtensionEnv:function(l,k){this.Extension(l.name,k,"environment")},Array:function(m,o,t,r,s,n,k,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){var l=(u.charAt(0)+u.charAt(u.length-1)).replace(/[^|:]/g,"");if(l!==""){q.arraydef.frame={"|":"solid",":":"dashed"}[l.charAt(0)];q.arraydef.framespacing=".5em .5ex"}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(k==="D"){q.arraydef.displaystyle=c}if(k==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=f}this.Push(m);return q},convertDelimiter:function(k){if(k){k=g.delimiter[k]}if(k==null){return null}if(k instanceof Array){k=k[0]}if(k.length===4){k=String.fromCharCode(parseInt(k,16))}return k},trimSpaces:function(k){if(typeof(k)!="string"){return k}return k.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var k=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(k){this.i+=k[1].length;return k[1]}else{this.i++;return" "}},GetArgument:function(l,m){switch(this.GetNext()){case"":if(!m){d.Error("Missing argument for "+l)}return null;case"}":if(!m){d.Error("Extra close brace or missing open brace")}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var k=++this.i,n=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":n++;break;case"}":if(n==0){d.Error("Extra close brace")}if(--n==0){return this.string.slice(k,this.i-1)}break}}d.Error("Missing close brace");break}return this.string.charAt(this.i++)},GetBrackets:function(l){if(this.GetNext()!="["){return""}var k=++this.i,m=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":m++;break;case"\\":this.i++;break;case"}":if(m--<=0){d.Error("Extra close brace while looking for ']'")}break;case"]":if(m==0){return this.string.slice(k,this.i-1)}break}}d.Error("Couldn't find closing
']' for argument to
"+l)},GetDelimiter:function(k){while(this.nextIsSpace()){this.i++}var l=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(l=="\\"){l+=this.GetCS(k)}if(g.delimiter[l]!=null){return this.convertDelimiter(l)}}d.Error("Missing or unrecognized delimiter
for "+k)},GetDimen:function(l){var m;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){m=this.GetArgument(l);if(m.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return m.replace(/ /g,"")}}else{m=this.string.slice(this.i);var k=m.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(k){this.i+=k[0].length;return k[1].replace(/ /g,"")}}d.Error("Missing dimension or its units
for "+l)},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error("Extra close brace
while looking
for "+o)}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error("Couldn
't find "+o+" for "+n)},ParseArg:function(k){return d.Parse(this.GetArgument(k),this.stack.env).mml()},ParseUpTo:function(k,l){return d.Parse(this.GetUpTo(k,l),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:f};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\$|\\\(/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(i.TeXAtom(d.Parse(q.slice(l,o-1)).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="\\"){r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(i.TeXAtom(d.Parse(q.slice(l,o-2)).mml().With(p)));n="";l=o}}}}}if(n!==""){d.Error("Math not terminated in text box")}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(l,k){l=l.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(l)).With(k)},SubstituteArgs:function(l,k){var o="";var n="";var p;var m=0;while(m<k.length){p=k.charAt(m++);if(p==="\\"){o+=p+k.charAt(m++)}else{if(p==="#"){p=k.charAt(m++);if(p==="#"){o+=p}else{if(!p.match(/[1-9]/)||p>l.length){d.Error("Illegal macro parameter reference")}n=this.AddArgs(this.AddArgs(n,o),l[p-1]);o=""}}else{o+=p}}}return this.AddArgs(n,o)},AddArgs:function(l,k){if(k.match(/^[a-z]/i)&&l.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){l+=" "}if(l.length+k.length>d.config.MAXBUFFER){d.Error("MathJax internal buffer size exceeded; is there a recursive macro call?")}return l+k}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:j,config:{MAXMACROS:10000,MAXBUFFER:5*1024},Translate:function(k){var l,n=k.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(MathJax.Hub.Browser.isKonqueror){n=n.replace(/</g,"<").replace(/>/g,">").replace(/&/g,"&")}var o=(k.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);n=d.prefilterMath(n,o,k);try{l=d.Parse(n).mml()}catch(m){if(!m.texError){throw m}l=this.formatError(m,n,o,k)}if(l.inferred){l=i.apply(MathJax.ElementJax,l.data)}else{l=i(l)}if(o){l.root.display="block"}return this.postfilterMath(l,o,k)},prefilterMath:function(l,m,k){return l.replace(/([_^]\s*\d)([0-9.,])/g,"$1 $2")},postfilterMath:function(l,m,k){this.combineRelations(l.root);return l},formatError:function(m,l,n,k){return i.merror(m.message.replace(/\n.*/,""))},Error:function(k){throw MathJax.Hub.Insert(Error(k),{texError:c})},Macro:function(k,l,m){g.macros[k]=["Macro"].concat([].slice.call(arguments,1))},combineRelations:function(l){for(var n=0,k=l.data.length;n<k;n++){if(l.data[n]){if(l.isa(i.mrow)){while(n+1<k&&l.data[n+1]&&l.data[n].isa(i.mo)&&l.data[n+1].isa(i.mo)&&l.data[n].Get("texClass")===i.TEXCLASS.REL&&l.data[n+1].Get("texClass")===i.TEXCLASS.REL){l.data[n].Append.apply(l.data[n],l.data[n+1].data);l.data.splice(n+1,1);k--}}if(!l.data[n].isToken){this.combineRelations(l.data[n])}}}}});d.loadComplete("jax.js")})(MathJax.InputJax.TeX);
52 MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var e="1.1";var a=MathJax.ElementJax.mml;var f=MathJax.InputJax.TeX;var c=f.Definitions;var d=f.Stack.Item;var b=function(g){return g.join("em ")+"em"};MathJax.Hub.Insert(c,{macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",a.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",a.LENGTH.NEGATIVETHICKMATHSPACE],intI:["Macro","\\mathchoice{\\!}{}{}{}\\!\\!\\int"],iiiint:["MultiIntegral","\\int\\intI\\intI\\intI"],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}}",1],ddddot:["Macro","\\mathop{#1}\\limits^{\\textstyle \\mathord{.}\\mathord{.}\\mathord{.}\\mathord{.}}",1],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["Macro","\\mathop{\\rm inj\\,lim}"],projlim:["Macro","\\mathop{\\rm proj\\,lim}"],varliminf:["Macro","\\mathop{\\underline{\\rm lim}}"],varlimsup:["Macro","\\mathop{\\overline{\\rm lim}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\rm lim\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0em",""],tbinom:["Genfrac","(",")","0em",1],dbinom:["Genfrac","(",")","0em",0],cfrac:"CFrac",shoveleft:["HandleShove",a.ALIGN.LEFT],shoveright:["HandleShove",a.ALIGN.RIGHT],xrightarrow:["xArrow",8594,5,6],xleftarrow:["xArrow",8592,7,3]},environment:{align:["AMSarray",null,true,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",b([5/18])],gather:["AMSarray",null,true,true,"c"],"gather*":["AMSarray",null,false,true,"c"],alignat:["AlignAt",null,true,true],"alignat*":["AlignAt",null,false,true],alignedat:["AlignAt",null,false,false],aligned:["Array",null,null,null,"rlrlrlrlrlrl",b([5/18,2,5/18,2,5/18,2,5/18,2,5/18,2,5/18]),".5em","D"],gathered:["Array",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,b([0,0,0,0]),"0.1em","S",1],smallmatrix:["Array",null,null,null,"c",b([1/3]),".2em","S",1]},delimiter:{"\\lvert":["2223",{texClass:a.TEXCLASS.OPEN}],"\\rvert":["2223",{texClass:a.TEXCLASS.CLOSE}],"\\lVert":["2225",{texClass:a.TEXCLASS.OPEN}],"\\rVert":["2225",{texClass:a.TEXCLASS.CLOSE}]}});f.Parse.Augment({HandleTag:function(h){var g=this.trimSpaces(this.GetArgument(h));if(g==="*"){g=this.GetArgument(h)}else{g="("+g+")"}if(this.stack.global.notag){f.Error(h+" not allowed in "+this.stack.global.notag+" environment")}if(this.stack.global.tag){f.Error("Multiple "+h)}this.stack.global.tag=a.mtd.apply(a,this.InternalMath(g))},HandleNoTag:function(g){if(this.stack.global.tag){delete this.stack.global.tag}},HandleDeclareOp:function(h){var g="";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}if(i.charAt(0)=="\\"){i=i.substr(1)}var j=this.GetArgument(h);j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");f.Definitions.macros[i]=["Macro","\\mathop{\\rm "+j+"}"+g]},HandleOperatorName:function(h){var g="\\nolimits";var i=this.trimSpaces(this.GetArgument(h));if(i=="*"){g="\\limits";i=this.trimSpaces(this.GetArgument(h))}i=i.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+i+"}"+g+" "+this.string.slice(this.i);this.i=0},HandleShove:function(h,g){var i=this.stack.Top();if(i.type!=="multline"||i.data.length){f.Error(h+" must come at the beginning of the line")}i.data.shove=g},CFrac:function(j){var g=this.trimSpaces(this.GetBrackets(j)),i=this.GetArgument(j),k=this.GetArgument(j);var h=a.mfrac(f.Parse("\\strut\\textstyle{"+i+"}",this.stack.env).mml(),f.Parse("\\strut\\textstyle{"+k+"}",this.stack.env).mml());g=({l:a.ALIGN.LEFT,r:a.ALIGN.RIGHT,"":""})[g];if(g==null){f.Error("Illegal alignment specified in "+j)}if(g){h.numalign=h.denomalign=g}this.Push(h)},Genfrac:function(h,j,o,l,g){if(j==null){j=this.GetDelimiterArg(h)}else{j=this.convertDelimiter(j)}if(o==null){o=this.GetDelimiterArg(h)}else{o=this.convertDelimiter(o)}if(l==null){l=this.GetArgument(h)}if(g==null){g=this.trimSpaces(this.GetArgument(h))}var k=this.ParseArg(h);var n=this.ParseArg(h);var i=a.mfrac(k,n);if(l!==""){i.linethickness=l}if(j||o){i=a.mfenced(i).With({open:j,close:o})}if(g!==""){var m=(["D","T","S","SS"])[g];if(m==null){f.Error("Bad math style for "+h)}i=a.mstyle(i);if(m==="D"){i.displaystyle=true;i.scriptlevel=0}else{i.displaystyle=false;i.scriptlevel=g-1}}this.Push(i)},Multline:function(h,g){this.Push(h);return d.multline().With({arraydef:{displaystyle:true,rowspacing:".5em",width:f.config.MultLineWidth,columnwidth:"100%",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AMSarray:function(i,h,g,k,j){this.Push(i);k=k.replace(/[^clr]/g,"").split("").join(" ");k=k.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return d.AMSarray(i.name,h,g,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:k,columnspacing:(j||"1em"),rowspacing:"3pt",side:f.config.TagSide,minlabelspacing:f.config.TagIndent}})},AlignAt:function(i,h,g){var j=this.GetArgument("\\begin{"+i.name+"}");if(j.match(/[^0-9]/)){f.Error("Argument to \\begin{"+i.name+"} must me a positive integer")}align="";spacing=[];while(j>0){align+="rl";spacing.push("0em 0em");j--}spacing=spacing.join(" ");if(g){return this.AMSarray(i,h,g,align,spacing)}return this.Array(i,null,null,align,spacing,".5em","D")},MultiIntegral:function(g,k){var j=this.GetNext();if(j==="\\"){var h=this.i;j=this.GetArgument(g);this.i=h;if(j==="\\limits"){if(g==="\\idotsint"){k="\\!\\!\\mathop{\\,\\,"+k+"}"}else{k="\\!\\!\\!\\mathop{\\,\\,\\,"+k+"}"}}}this.string=k+" "+this.string.slice(this.i);this.i=0},xArrow:function(i,m,k,g){var j={width:"+"+(k+g)+"mu",lspace:k+"mu"};var n=this.GetBrackets(i),o=this.ParseArg(i);var p=a.mo(a.chars(String.fromCharCode(m))).With({stretchy:true,texClass:a.TEXCLASS.REL});var h=a.munderover(p);h.SetData(h.over,a.mpadded(o).With(j).With({voffset:".15em"}));if(n){n=f.Parse(n,this.stack.env).mml();h.SetData(h.under,a.mpadded(n).With(j).With({voffset:"-.24em"}))}this.Push(h)},GetDelimiterArg:function(g){var h=this.trimSpaces(this.GetArgument(g));if(h==""){return null}if(!c.delimiter[h]){f.Error("Missing or unrecognized delimiter for "+g)}return this.convertDelimiter(h)}});d.multline=d.array.Subclass({type:"multline",EndEntry:function(){var g=a.mtd.apply(a,this.data);if(this.data.shove){g.columnalign=this.data.shove}this.row.push(g);this.data=[]},EndRow:function(){if(this.row.length!=1){f.Error("multline rows must have exactly one column")}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var h=this.table.length-1,j;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=a.ALIGN.LEFT}if(!this.table[h][0].columnalign){this.table[h][0].columnalign=a.ALIGN.RIGHT}var g=a.mtr;if(this.global.tag){this.table[0]=[this.global.tag].concat(this.table[0]);delete this.global.tag;g=a.mlabeledtr}this.table[0]=g.apply(a,this.table[0]);for(j=1,h=this.table.length;j<h;j++){this.table[j]=a.mtr.apply(a,this.table[j])}}}});d.AMSarray=d.array.Subclass({type:"AMSarray",Init:function(j,i,h,g){this.SUPER(arguments).Init.apply(this);this.numbered=i;this.save_notag=g.global.notag;g.global.notag=(h?null:j)},EndRow:function(){var g=a.mtr;if(this.global.tag){this.row=[this.global.tag].concat(this.row);g=a.mlabeledtr;delete this.global.tag}this.table.push(g.apply(a,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notag=this.save_notag}});d.start.Augment({oldCheckItem:d.start.prototype.checkItem,checkItem:function(h){if(h.type==="stop"){var g=this.mmlData();if(this.global.tag){var j=[this.global.tag,a.mtd(g)];delete this.global.tag;var i={side:f.config.TagSide,minlabelspacing:f.config.TagIndent,columnalign:g.displayAlign};if(g.displayAlign===a.INDENTALIGN.LEFT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth=g.displayIndent+" fit";i.columnspacing="0";j=[j[0],a.mtd(),j[1]]}}else{if(g.displayAlign===a.INDENTALIGN.RIGHT){i.width="100%";if(g.displayIndent&&!String(g.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){i.columnwidth="fit "+g.displayIndent;i.columnspacing="0";j[2]=a.mtd()}}}g=a.mtable(a.mlabeledtr.apply(a,j)).With(i)}return d.mml(g)}return this.SUPER(arguments).checkItem.call(this,h)}});MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");
54 MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b="1.1.2";var a=MathJax.ElementJax.mml;MathJax.Hub.Insert(MathJax.InputJax.TeX.Definitions,{mathchar0mi:{digamma:"03DD",varkappa:"03F0",varGamma:["0393",{mathvariant:a.VARIANT.ITALIC}],varDelta:["0394",{mathvariant:a.VARIANT.ITALIC}],varTheta:["0398",{mathvariant:a.VARIANT.ITALIC}],varLambda:["039B",{mathvariant:a.VARIANT.ITALIC}],varXi:["039E",{mathvariant:a.VARIANT.ITALIC}],varPi:["03A0",{mathvariant:a.VARIANT.ITALIC}],varSigma:["03A3",{mathvariant:a.VARIANT.ITALIC}],varUpsilon:["03A5",{mathvariant:a.VARIANT.ITALIC}],varPhi:["03A6",{mathvariant:a.VARIANT.ITALIC}],varPsi:["03A8",{mathvariant:a.VARIANT.ITALIC}],varOmega:["03A9",{mathvariant:a.VARIANT.ITALIC}],beth:"2136",gimel:"2137",daleth:"2138",backprime:["2035",{variantForm:true}],hslash:["210F",{variantForm:true}],varnothing:["2205",{variantForm:true}],blacktriangle:"25B2",triangledown:"25BD",blacktriangledown:"25BC",square:"25A1",Box:"25A1",blacksquare:"25A0",lozenge:"25CA",Diamond:"25CA",blacklozenge:"29EB",circledS:["24C8",{mathvariant:a.VARIANT.NORMAL}],bigstar:"2605",sphericalangle:"2222",measuredangle:"2221",nexists:"2204",complement:"2201",mho:"2127",eth:["00F0",{mathvariant:a.VARIANT.NORMAL}],Finv:"2132",diagup:"2571",Game:"2141",diagdown:"2572",Bbbk:["006B",{mathvariant:a.VARIANT.DOUBLESTRUCK}],yen:"00A5",circledR:"00AE",checkmark:"2713",maltese:"2720"},mathchar0mo:{dotplus:"2214",ltimes:"22C9",smallsetminus:["2216",{variantForm:true}],rtimes:"22CA",Cap:"22D2",doublecap:"22D2",leftthreetimes:"22CB",Cup:"22D3",doublecup:"22D3",rightthreetimes:"22CC",barwedge:"22BC",curlywedge:"22CF",veebar:"22BB",curlyvee:"22CE",doublebarwedge:"2A5E",boxminus:"229F",circleddash:"229D",boxtimes:"22A0",circledast:"229B",boxdot:"22A1",circledcirc:"229A",boxplus:"229E",centerdot:"22C5",divideontimes:"22C7",intercal:"22BA",leqq:"2266",geqq:"2267",leqslant:"2A7D",geqslant:"2A7E",eqslantless:"2A95",eqslantgtr:"2A96",lesssim:"2272",gtrsim:"2273",lessapprox:"2A85",gtrapprox:"2A86",approxeq:"224A",lessdot:"22D6",gtrdot:"22D7",lll:"22D8",llless:"22D8",ggg:"22D9",gggtr:"22D9",lessgtr:"2276",gtrless:"2277",lesseqgtr:"22DA",gtreqless:"22DB",lesseqqgtr:"2A8B",gtreqqless:"2A8C",doteqdot:"2251",Doteq:"2251",eqcirc:"2256",risingdotseq:"2253",circeq:"2257",fallingdotseq:"2252",triangleq:"225C",backsim:"223D",thicksim:["223C",{variantForm:true}],backsimeq:"22CD",thickapprox:"2248",subseteqq:"2AC5",supseteqq:"2AC6",Subset:"22D0",Supset:"22D1",sqsubset:"228F",sqsupset:"2290",preccurlyeq:"227C",succcurlyeq:"227D",curlyeqprec:"22DE",curlyeqsucc:"22DF",precsim:"227E",succsim:"227F",precapprox:"2AB7",succapprox:"2AB8",vartriangleleft:"22B2",lhd:"22B2",vartriangleright:"22B3",rhd:"22B3",trianglelefteq:"22B4",unlhd:"22B4",trianglerighteq:"22B5",unrhd:"22B5",vDash:"22A8",Vdash:"22A9",Vvdash:"22AA",smallsmile:"2323",shortmid:["2223",{variantForm:true}],smallfrown:"2322",shortparallel:["2225",{variantForm:true}],bumpeq:"224F",between:"226C",Bumpeq:"224E",pitchfork:"22D4",varpropto:"221D",backepsilon:"220D",blacktriangleleft:"25C0",blacktriangleright:"25B6",therefore:"2234",because:"2235",eqsim:"2242",vartriangle:["25B3",{variantForm:true}],Join:"22C8",nless:"226E",ngtr:"226F",nleq:"2270",ngeq:"2271",nleqslant:["2A87",{variantForm:true}],ngeqslant:["2A88",{variantForm:true}],nleqq:["2270",{variantForm:true}],ngeqq:["2271",{variantForm:true}],lneq:"2A87",gneq:"2A88",lneqq:"2268",gneqq:"2269",lvertneqq:["2268",{variantForm:true}],gvertneqq:["2269",{variantForm:true}],lnsim:"22E6",gnsim:"22E7",lnapprox:"2A89",gnapprox:"2A8A",nprec:"2280",nsucc:"2281",npreceq:["22E0",{variantForm:true}],nsucceq:["22E1",{variantForm:true}],precneqq:"2AB5",succneqq:"2AB6",precnsim:"22E8",succnsim:"22E9",precnapprox:"2AB9",succnapprox:"2ABA",nsim:"2241",ncong:"2246",nshortmid:["2224",{variantForm:true}],nshortparallel:["2226",{variantForm:true}],nmid:"2224",nparallel:"2226",nvdash:"22AC",nvDash:"22AD",nVdash:"22AE",nVDash:"22AF",ntriangleleft:"22EA",ntriangleright:"22EB",ntrianglelefteq:"22EC",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigarrow:"21DD",leadsto:"21DD",dashrightarrow:"21E2",dashleftarrow:"21E0",nleftarrow:"219A",nrightarrow:"219B",nLeftarrow:"21CD",nRightarrow:"21CF",nleftrightarrow:"21AE",nLeftrightarrow:"21CE"},delimiter:{"\\ulcorner":"250C","\\urcorner":"2510","\\llcorner":"2514","\\lrcorner":"2518"},macros:{implies:["Macro","\\;\\Longrightarrow\\;"],impliedby:["Macro","\\;\\Longleftarrow\\;"]}});var c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}})});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.OutputJax["HTML-CSS"];var b=a.FONTDATA.VARIANT;if(a.fontInUse==="TeX"){b["-TeX-variant"]={fonts:["MathJax_AMS","MathJax_Main","MathJax_Size1"],remap:{8808:57356,8809:57357,8816:57361,8817:57358,10887:57360,10888:57359,8740:57350,8742:57351,8840:57366,8841:57368,8842:57370,8843:57371,10955:57367,10956:57369,988:57352,1008:57353}};if(a.msieIE6){MathJax.Hub.Insert(b["-TeX-variant"].remap,{8592:[58049,"-WinIE6"],8594:[58048,"-WinIE6"],8739:[58050,"-WinIE6"],8741:[58051,"-WinIE6"],8764:[58052,"-WinIE6"],9651:[58067,"-WinIE6"]})}}if(a.fontInUse==="STIX"){MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX.Definitions;c.mathchar0mi.varnothing="2205";c.mathchar0mi.hslash="210F";c.mathchar0mi.blacktriangle="25B4";c.mathchar0mi.blacktriangledown="25BE";c.mathchar0mi.square="25FB";c.mathchar0mi.blacksquare="25FC";c.mathchar0mi.vartriangle=["25B3",{mathsize:"71%"}];c.mathchar0mi.triangledown=["25BD",{mathsize:"71%"}];c.mathchar0mo.blacktriangleleft="25C2";c.mathchar0mo.blacktriangleright="25B8";c.mathchar0mo.smallsetminus="2216";MathJax.Hub.Insert(b["-STIX-variant"],{remap:{10887:57360,10888:57359,8816:57361,8817:57358,8928:57419,8929:57423,8840:57366,8841:57368}})})}MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
56 MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_HTML.js");