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/ *
* / M a t h J a x / c o n f i g / M M L _ H T M L o r M M L - f u l l . j s
*
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* Copyright ( c ) 2010 - 2015 The MathJax Consortium
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*
* Part of the MathJax library .
* See http : //www.mathjax.org for details.
*
* Licensed under the Apache License , Version 2.0 ;
* you may not use this file except in compliance with the License .
*
* http : //www.apache.org/licenses/LICENSE-2.0
* /
MathJax . Hub . Config ( { delayJaxRegistration : true } ) ;
MathJax . Ajax . Preloading (
"[MathJax]/jax/input/MathML/config.js" ,
"[MathJax]/jax/output/HTML-CSS/config.js" ,
"[MathJax]/jax/output/NativeMML/config.js" ,
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"[MathJax]/jax/output/PreviewHTML/config.js" ,
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"[MathJax]/config/MMLorHTML.js" ,
"[MathJax]/extensions/mml2jax.js" ,
"[MathJax]/extensions/MathEvents.js" ,
"[MathJax]/extensions/MathZoom.js" ,
"[MathJax]/extensions/MathMenu.js" ,
"[MathJax]/jax/element/mml/jax.js" ,
"[MathJax]/extensions/toMathML.js" ,
"[MathJax]/jax/input/MathML/jax.js" ,
"[MathJax]/jax/output/NativeMML/jax.js" ,
"[MathJax]/jax/output/HTML-CSS/jax.js" ,
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"[MathJax]/jax/output/HTML-CSS/autoload/mtable.js" ,
"[MathJax]/jax/output/PreviewHTML/jax.js" ,
"[MathJax]/extensions/fast-preview.js" ,
"[MathJax]/extensions/AssistiveMML.js"
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) ;
MathJax . Hub . Config ( { "v1.0-compatible" : false } ) ;
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MathJax . InputJax . MathML = MathJax . InputJax ( { id : "MathML" , version : "2.6.1" , directory : MathJax . InputJax . directory + "/MathML" , extensionDir : MathJax . InputJax . extensionDir + "/MathML" , entityDir : MathJax . InputJax . directory + "/MathML/entities" , config : { useMathMLspacing : false } } ) ; MathJax . InputJax . MathML . Register ( "math/mml" ) ; MathJax . InputJax . MathML . loadComplete ( "config.js" ) ;
MathJax . OutputJax [ "HTML-CSS" ] = MathJax . OutputJax ( { id : "HTML-CSS" , version : "2.6.1" , directory : MathJax . OutputJax . directory + "/HTML-CSS" , extensionDir : MathJax . OutputJax . extensionDir + "/HTML-CSS" , autoloadDir : MathJax . OutputJax . directory + "/HTML-CSS/autoload" , fontDir : MathJax . OutputJax . directory + "/HTML-CSS/fonts" , webfontDir : MathJax . OutputJax . fontDir + "/HTML-CSS" , config : { noReflows : true , matchFontHeight : true , scale : 100 , minScaleAdjust : 50 , availableFonts : [ "STIX" , "TeX" ] , preferredFont : "TeX" , webFont : "TeX" , imageFont : "TeX" , undefinedFamily : "STIXGeneral,'Arial Unicode MS',serif" , mtextFontInherit : false , EqnChunk : ( MathJax . Hub . Browser . isMobile ? 10 : 50 ) , EqnChunkFactor : 1.5 , EqnChunkDelay : 100 , linebreaks : { automatic : false , width : "container" } , styles : { ".MathJax_Display" : { "text-align" : "center" , margin : "1em 0em" } , ".MathJax .merror" : { "background-color" : "#FFFF88" , color : "#CC0000" , border : "1px solid #CC0000" , padding : "1px 3px" , "font-style" : "normal" , "font-size" : "90%" } , ".MathJax .MJX-monospace" : { "font-family" : "monospace" } , ".MathJax .MJX-sans-serif" : { "font-family" : "sans-serif" } , "#MathJax_Tooltip" : { "background-color" : "InfoBackground" , color : "InfoText" , border : "1px solid black" , "box-shadow" : "2px 2px 5px #AAAAAA" , "-webkit-box-shadow" : "2px 2px 5px #AAAAAA" , "-moz-box-shadow" : "2px 2px 5px #AAAAAA" , "-khtml-box-shadow" : "2px 2px 5px #AAAAAA" , filter : "progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')" , padding : "3px 4px" , "z-index" : 401 } } } } ) ; if ( MathJax . Hub . Browser . isMSIE && document . documentMode >= 9 ) { delete MathJax . OutputJax [ "HTML-CSS" ] . config . styles [ "#MathJax_Tooltip" ] . filter } if ( ! MathJax . Hub . config . delayJaxRegistration ) { MathJax . OutputJax [ "HTML-CSS" ] . Register ( "jax/mml" ) } MathJax . Hub . Register . StartupHook ( "End Config" , [ function ( b , c ) { var a = b . Insert ( { minBrowserVersion : { Firefox : 3 , Opera : 9.52 , MSIE : 6 , Chrome : 0.3 , Safari : 2 , Konqueror : 4 } , inlineMathDelimiters : [ "$" , "$" ] , displayMathDelimiters : [ "$$" , "$$" ] , multilineDisplay : true , minBrowserTranslate : function ( f ) { var e = b . getJaxFor ( f ) , k = [ "[Math]" ] , j ; var h = document . createElement ( "span" , { className : "MathJax_Preview" } ) ; if ( e . inputJax === "TeX" ) { if ( e . root . Get ( "displaystyle" ) ) { j = a . displayMathDelimiters ; k = [ j [ 0 ] + e . originalText + j [ 1 ] ] ; if ( a . multilineDisplay ) { k = k [ 0 ] . split ( /\n/ ) } } else { j = a . inlineMathDelimiters ; k = [ j [ 0 ] + e . originalText . replace ( /^\s+/ , "" ) . replace ( /\s+$/ , "" ) + j [ 1 ] ] } } for ( var g = 0 , d = k . length ; 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 ( [ "MathJaxNotSupported" , "Your browser does not support MathJax" ] , null , 4000 ) ; b . Startup . signal . Post ( "MathJax not supported" ) } } , MathJax . Hub , MathJax . OutputJax [ "HTML-CSS" ] ] ) ; MathJax . OutputJax [ "HTML-CSS" ] . loadComplete ( "config.js" ) ;
MathJax . OutputJax . NativeMML = MathJax . OutputJax ( { id : "NativeMML" , version : "2.6.1" , directory : MathJax . OutputJax . directory + "/NativeMML" , extensionDir : MathJax . OutputJax . extensionDir + "/NativeMML" , config : { matchFontHeight : true , scale : 100 , minScaleAdjust : 50 , styles : { "div.MathJax_MathML" : { "text-align" : "center" , margin : ".75em 0px" } } } } ) ; if ( ! MathJax . Hub . config . delayJaxRegistration ) { MathJax . OutputJax . NativeMML . Register ( "jax/mml" ) } MathJax . OutputJax . NativeMML . loadComplete ( "config.js" ) ;
MathJax . OutputJax . PreviewHTML = MathJax . OutputJax ( { id : "PreviewHTML" , version : "2.6.1" , directory : MathJax . OutputJax . directory + "/PreviewHTML" , extensionDir : MathJax . OutputJax . extensionDir + "/PreviewHTML" , noFastPreview : true , config : { scale : 100 , minScaleAdjust : 50 , mtextFontInherit : false , linebreaks : { automatic : false , width : "container" } } } ) ; if ( ! MathJax . Hub . config . delayJaxRegistration ) { MathJax . OutputJax . PreviewHTML . Register ( "jax/mml" ) } MathJax . OutputJax . PreviewHTML . loadComplete ( "config.js" ) ;
( function ( c , g ) { var f = "2.6.0" ; var a = MathJax . Hub . CombineConfig ( "MMLorHTML" , { prefer : { MSIE : "MML" , Firefox : "HTML" , Opera : "HTML" , Chrome : "HTML" , Safari : "HTML" , other : "HTML" } } ) ; var e = { Firefox : 3 , Opera : 9.52 , MSIE : 6 , Chrome : 0.3 , Safari : 2 , Konqueror : 4 } ; var b = ( g . version === "0.0" || g . versionAtLeast ( e [ g ] || 0 ) ) ; var d = ( g . isFirefox && g . versionAtLeast ( "1.5" ) ) || ( g . isMSIE && g . hasMathPlayer ) || ( g . isSafari && g . versionAtLeast ( "5.0" ) ) || ( g . isOpera && g . versionAtLeast ( "9.52" ) ) ; c . Register . StartupHook ( "End Config" , function ( ) { var h = ( a . prefer && typeof ( a . prefer ) === "object" ? a . prefer [ MathJax . Hub . Browser ] || a . prefer . other || "HTML" : a . prefer ) ; if ( b || d ) { if ( d && ( h === "MML" || ! b ) ) { if ( MathJax . OutputJax . NativeMML ) { MathJax . OutputJax . NativeMML . Register ( "jax/mml" ) } else { c . config . jax . unshift ( "output/NativeMML" ) } c . Startup . signal . Post ( "NativeMML output selected" ) } else { if ( MathJax . OutputJax [ "HTML-CSS" ] ) { MathJax . OutputJax [ "HTML-CSS" ] . Register ( "jax/mml" ) } else { c . config . jax . unshift ( "output/HTML-CSS" ) } c . Startup . signal . Post ( "HTML-CSS output selected" ) } } else { c . PreProcess . disabled = true ; c . prepareScripts . disabled = true ; MathJax . Message . Set ( [ "MathJaxNotSupported" , "Your browser does not support MathJax" ] , null , 4000 ) ; c . Startup . signal . Post ( "MathJax not supported" ) } } ) } ) ( MathJax . Hub , MathJax . Hub . Browser ) ; MathJax . Ajax . loadComplete ( "[MathJax]/config/MMLorHTML.js" ) ;
MathJax . Extension . mml2jax = { version : "2.6.0" , config : { preview : "mathml" } , MMLnamespace : "http://www.w3.org/1998/Math/MathML" , PreProcess : function ( e ) { if ( ! this . configured ) { this . config = MathJax . Hub . CombineConfig ( "mml2jax" , this . config ) ; if ( this . config . Augment ) { MathJax . Hub . Insert ( this , this . config . Augment ) } this . InitBrowser ( ) ; this . configured = true } if ( typeof ( e ) === "string" ) { e = document . getElementById ( e ) } if ( ! e ) { e = document . body } var h = [ ] ; this . PushMathElements ( h , e , "math" ) ; this . PushMathElements ( h , e , "math" , this . MMLnamespace ) ; var d , b ; if ( typeof ( document . namespaces ) !== "undefined" ) { try { for ( d = 0 , b = document . namespaces . length ; d < b ; d ++ ) { var f = document . namespaces [ d ] ; if ( f . urn === this . MMLnamespace ) { this . PushMathElements ( h , e , f . name + ":math" ) } } } catch ( g ) { } } else { var c = document . getElementsByTagName ( "html" ) [ 0 ] ; if ( c ) { for ( d = 0 , b = c . attributes . length ; d < b ; d ++ ) { var a = c . attributes [ d ] ; if ( a . nodeName . substr ( 0 , 6 ) === "xmlns:" && a . nodeValue === this . MMLnamespace ) { this . PushMathElements ( h , e , a . nodeName . substr ( 6 ) + ":math" ) } } } } this . ProcessMathArray ( h ) } , PushMathElements : function ( f , d , a , c ) { var h , g = MathJax . Hub . config . preRemoveClass ; if ( c ) { if ( ! d . getElementsByTagNameNS ) { return } h = d . getElementsByTagNameNS ( c , a ) } else { h = d . getElementsByTagName ( a ) } for ( var e = 0 , b = h . length ; e < b ; e ++ ) { var j = h [ e ] . parentNode ; if ( j && j . className !== g && ! j . isMathJax && ! h [ e ] . prefix === ! c ) { f . push ( h [ e ] ) } } } , ProcessMathArray : function ( c ) { var b , a = c . length ; if ( a ) { if ( this . MathTagBug ) { for ( b = 0 ; b < a ; b ++ ) { if ( c [ b ] . nodeName === "MATH" ) { this . ProcessMathFlattened ( c [ b ] ) } else { this . ProcessMath ( c [ b ] ) } } } else { for ( b = 0 ; b < a ; b ++ ) { this . ProcessMath ( c [ b ] ) } } } } , ProcessMath : function ( e ) { var d = e . parentNode ; if ( ! d || d . className === MathJax . Hub . config . preRemoveClass ) { return } var a = document . createElement ( "script" ) ; a . type = "math/mml" ; d . insertBefore ( a , e ) ; if ( this . AttributeBug ) { var b = this . OuterHTML ( e ) ; if ( this . CleanupHTML ) { b = b . replace ( /<\?import .*?>/i , "" ) . replace ( /<\?xml:namespace .*?\/>/i , "" ) ; b = b . replace ( / /g , " " ) } MathJax . HTML . setScript ( a , b ) ; d . removeChild ( e ) } else { var c = MathJax . HTML . Element ( "span" ) ; c . appendChild ( e ) ; MathJax . HTML . setScript ( a , c . innerHTML ) } if ( this . config . preview !== "none" ) { this . createPreview ( e , a ) } } , ProcessMathFlattened : function ( f ) { var d = f . parentNode ; if ( ! d || d . className === MathJax . Hub . config . preRemoveClass ) { return } var b = document . createElement ( "script" ) ; b . type = "math/mml" ; d . insertBefore ( b , f ) ; var c = "" , e , a = f ; while ( f && f . nodeName !== "/MATH" ) { e = f ; f = f . nextSibling ; c += this . NodeHTML ( e ) ; e . parentNode . removeChild ( e ) } if ( f && f . nodeName === "/MATH" ) { f . parentNode . removeChild ( f ) } b . text = c + "</math>" ; if ( this . config . preview !== "none" ) { this . createPreview ( a , b ) } } , NodeHTML : function ( e ) { var c , b , a ; if ( e . nodeName === "#text" ) { c = this . quoteHTML ( e . nodeValue ) } else { if ( e . nodeName === "#comment" ) { c = "<!--" + e . nodeValue + "-->" } else { c = "<" + e . nodeName . toLowerCase ( ) ; for ( b = 0 , a = e . attributes . length ; b < a ; b ++ ) { var d = e . attributes [ b ] ; if ( d . specified && d . nodeName . substr ( 0 , 10 ) !== "_moz-math-" ) { c += " " + d . nodeName . toLowerCase ( ) . replace ( /xmlns:xmlns/ , "xmlns" ) + "=" ; var f = d . nodeValue ; if ( f == null && d . nodeName === "style" && e . style ) { f = e . style . cssText } c += '"' + this . quoteHTML ( f ) + '"' } } c += ">" ; if ( e . outerHTML != null && e . outerHTML . match ( /(.<\/[A-Z]+>|\/>)$/ ) ) { for ( b = 0 , a = e . childNodes . length ; b < a ; b ++ ) { c += this . OuterHTML ( e . childNodes [ b ] ) } c += "</" + e . nodeName . toLowerCase ( ) + ">" } } } return c } , OuterHTML : function ( d ) { if ( d . nodeName . charAt ( 0 ) === "#" ) { return this . NodeHTML ( d ) } if ( ! this . AttributeBug ) { return d . outerHTML } var c = this . NodeHTML ( d ) ; for ( var b = 0 , a = d . childNodes . length ; b < a ; b ++ ) { c += this . OuterHTML ( d . childNodes [ b ] ) } c += "</" + d . nodeName . toLowerCase ( ) + ">" ; return c } , quoteHTML : function ( a ) { if ( a == null ) { a = "" } return a . replace ( /&/g , "&" ) . replace ( /</g , "<" ) . replace ( />/g , ">" ) . replace ( /\"/g , """ ) } , createPreview : function ( f , b ) { var g = this . config . preview ; if ( g === "none" ) { return } var a = false ; if ( g === "mathml" ) { a = true ; if ( this . MathTagBug ) { g = "alttext" } else { g = f . cloneNode ( true ) } } if ( g === "alttext" || g === "altimg" ) { a = true ; var c = this . filterPreview ( f . getAttribute ( "alttext" ) ) ; if ( g === "alttext" ) { if ( c != null ) { g = MathJax . HTML . TextNode ( c ) } else { g = null } } else { var h = f . getAttribute ( "altimg" ) ; if ( h != null ) { var e = { width : f . getAttribute ( "altimg-width" ) , height : f . getAttribute ( "altimg-height" ) } ; g = MathJax . HTML . Element ( "img" ,
( function ( d , h , l , g , m , b , j ) { var p = "2.6.0" ; var i = MathJax . Extension ; var c = i . MathEvents = { version : p } ; var k = d . config . menuSettings ; var o = { hover : 500 , frame : { x : 3.5 , y : 5 , bwidth : 1 , bcolor : "#A6D" , hwidth : "15px" , hcolor : "#83A" } , button : { x : - 6 , y : - 3 , wx : - 2 } , fadeinInc : 0.2 , fadeoutInc : 0.05 , fadeDelay : 50 , fadeoutStart : 400 , fadeoutDelay : 15 * 1000 , styles : { ".MathJax_Hover_Frame" : { "border-radius" : ".25em" , "-webkit-border-radius" : ".25em" , "-moz-border-radius" : ".25em" , "-khtml-border-radius" : ".25em" , "box-shadow" : "0px 0px 15px #83A" , "-webkit-box-shadow" : "0px 0px 15px #83A" , "-moz-box-shadow" : "0px 0px 15px #83A" , "-khtml-box-shadow" : "0px 0px 15px #83A" , border : "1px solid #A6D ! important" , display : "inline-block" , position : "absolute" } , ".MathJax_Menu_Button .MathJax_Hover_Arrow" : { position : "absolute" , cursor : "pointer" , display : "inline-block" , border : "2px solid #AAA" , "border-radius" : "4px" , "-webkit-border-radius" : "4px" , "-moz-border-radius" : "4px" , "-khtml-border-radius" : "4px" , "font-family" : "'Courier New',Courier" , "font-size" : "9px" , color : "#F0F0F0" } , ".MathJax_Menu_Button .MathJax_Hover_Arrow span" : { display : "block" , "background-color" : "#AAA" , border : "1px solid" , "border-radius" : "3px" , "line-height" : 0 , padding : "4px" } , ".MathJax_Hover_Arrow:hover" : { color : "white!important" , border : "2px solid #CCC!important" } , ".MathJax_Hover_Arrow:hover span" : { "background-color" : "#CCC!important" } } } ; var n = c . Event = { LEFTBUTTON : 0 , RIGHTBUTTON : 2 , MENUKEY : "altKey" , KEY : { RETURN : 13 , ESCAPE : 27 , SPACE : 32 , LEFT : 37 , UP : 38 , RIGHT : 39 , DOWN : 40 } , Mousedown : function ( q ) { return n . Handler ( q , "Mousedown" , this ) } , Mouseup : function ( q ) { return n . Handler ( q , "Mouseup" , this ) } , Mousemove : function ( q ) { return n . Handler ( q , "Mousemove" , this ) } , Mouseover : function ( q ) { return n . Handler ( q , "Mouseover" , this ) } , Mouseout : function ( q ) { return n . Handler ( q , "Mouseout" , this ) } , Click : function ( q ) { return n . Handler ( q , "Click" , this ) } , DblClick : function ( q ) { return n . Handler ( q , "DblClick" , this ) } , Menu : function ( q ) { return n . Handler ( q , "ContextMenu" , this ) } , Handler : function ( t , r , s ) { if ( l . loadingMathMenu ) { return n . False ( t ) } var q = b [ s . jaxID ] ; if ( ! t ) { t = window . event } t . isContextMenu = ( r === "ContextMenu" ) ; if ( q [ r ] ) { return q [ r ] ( t , s ) } if ( i . MathZoom ) { return i . MathZoom . HandleEvent ( t , r , s ) } } , False : function ( q ) { if ( ! q ) { q = window . event } if ( q ) { if ( q . preventDefault ) { q . preventDefault ( ) } else { q . returnValue = false } if ( q . stopPropagation ) { q . stopPropagation ( ) } q . cancelBubble = true } return false } , Keydown : function ( r , q ) { if ( ! r ) { r = window . event } if ( r . keyCode === n . KEY . SPACE ) { n . ContextMenu ( r , this ) } } , ContextMenu : function ( t , E , w ) { var B = b [ E . jaxID ] , v = B . getJaxFromMath ( E ) ; var F = ( B . config . showMathMenu != null ? B : d ) . config . showMathMenu ; if ( ! F || ( k . context !== "MathJax" && ! w ) ) { return } if ( c . msieEventBug ) { t = window . event || t } n . ClearSelection ( ) ; f . ClearHoverTimer ( ) ; if ( v . hover ) { if ( v . hover . remove ) { clearTimeout ( v . hover . remove ) ; delete v . hover . remove } v . hover . nofade = true } var u = MathJax . Menu ; var G , D ; if ( u ) { if ( u . loadingDomain ) { return n . False ( t ) } G = m . loadDomain ( "MathMenu" ) ; if ( ! G ) { u . jax = v ; var r = u . menu . Find ( "Show Math As" ) . submenu ; r . items [ 0 ] . name = v . sourceMenuTitle ; r . items [ 0 ] . format = ( v . sourceMenuFormat || "MathML" ) ; r . items [ 1 ] . name = j [ v . inputJax ] . sourceMenuTitle ; r . items [ 5 ] . disabled = ! j [ v . inputJax ] . annotationEncoding ; var A = r . items [ 2 ] ; A . disabled = true ; var q = A . submenu . items ; annotationList = MathJax . Hub . Config . semanticsAnnotations ; for ( var z = 0 , y = q . length ; z < y ; z ++ ) { var s = q [ z ] . name [ 1 ] ; if ( v . root && v . root . getAnnotation ( s ) !== null ) { A . disabled = false ; q [ z ] . hidden = false } else { q [ z ] . hidden = true } } var x = u . menu . Find ( "Math Settings" , "MathPlayer" ) ; x . hidden = ! ( v . outputJax === "NativeMML" && d . Browser . hasMathPlayer ) ; return u . menu . Post ( t ) } u . loadingDomain = true ; D = function ( ) { delete u . loadingDomain } } else { if ( l . loadingMathMenu ) { return n . False ( t ) } l . loadingMathMenu = true ; G = l . Require ( "[MathJax]/extensions/MathMenu.js" ) ; D = function ( ) { delete l . loadingMathMenu ; if ( ! MathJax . Menu ) { MathJax . Menu = { } } } } var C = { pageX : t . pageX , pageY : t . pageY , clientX : t . clientX , clientY : t . clientY } ; g . Queue ( G , D , [ "ContextMenu" , n , C , E , w ] ) ; return n . False ( t ) } , AltContextMenu : function ( s , r ) { var t = b [ r . jaxID ] ; var q = ( t . config . showMathMenu != null ? t : d ) . config . showMathMenu ; if ( q ) { q = ( t . config . showMathMenuMSIE != null ? t : d ) . config . showMathMenuMSIE ; if ( k . context === "MathJax" && ! k . mpContext && q ) {
( function ( a , d , f , c , j ) { var k = "2.6.0" ; var i = a . CombineConfig ( "MathZoom" , { styles : { "#MathJax_Zoom" : { position : "absolute" , "background-color" : "#F0F0F0" , overflow : "auto" , display : "block" , "z-index" : 301 , padding : ".5em" , border : "1px solid black" , margin : 0 , "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" , "-webkit-box-sizing" : "content-box" , "-moz-box-sizing" : "content-box" , "box-sizing" : "content-box" , "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)" } , "#MathJax_ZoomFrame" : { position : "relative" , display : "inline-block" , height : 0 , width : 0 } , "#MathJax_ZoomEventTrap" : { position : "absolute" , left : 0 , top : 0 , "z-index" : 302 , display : "inline-block" , border : 0 , padding : 0 , margin : 0 , "background-color" : "white" , opacity : 0 , filter : "alpha(opacity=0)" } } } ) ; var e , b , g ; MathJax . Hub . Register . StartupHook ( "MathEvents Ready" , function ( ) { g = MathJax . Extension . MathEvents . Event ; e = MathJax . Extension . MathEvents . Event . False ; b = MathJax . Extension . MathEvents . Hover } ) ; var h = MathJax . Extension . MathZoom = { version : k , settings : a . config . menuSettings , scrollSize : 18 , HandleEvent : function ( n , l , m ) { if ( h . settings . CTRL && ! n . ctrlKey ) { return true } if ( h . settings . ALT && ! n . altKey ) { return true } if ( h . settings . CMD && ! n . metaKey ) { return true } if ( h . settings . Shift && ! n . shiftKey ) { return true } if ( ! h [ l ] ) { return true } return h [ l ] ( n , m ) } , Click : function ( m , l ) { if ( this . settings . zoom === "Click" ) { return this . Zoom ( m , l ) } } , DblClick : function ( m , l ) { if ( this . settings . zoom === "Double-Click" || this . settings . zoom === "DoubleClick" ) { return this . Zoom ( m , l ) } } , Hover : function ( m , l ) { if ( this . settings . zoom === "Hover" ) { this . Zoom ( m , l ) ; return true } return false } , Zoom : function ( o , u ) { this . Remove ( ) ; b . ClearHoverTimer ( ) ; g . ClearSelection ( ) ; var s = MathJax . OutputJax [ u . jaxID ] ; var p = s . getJaxFromMath ( u ) ; if ( p . hover ) { b . UnHover ( p ) } var q = this . findContainer ( u ) ; var l = Math . floor ( 0.85 * q . clientWidth ) , t = Math . max ( document . body . clientHeight , document . documentElement . clientHeight ) ; if ( this . getOverflow ( q ) !== "visible" ) { t = Math . min ( q . clientHeight , t ) } t = Math . floor ( 0.85 * t ) ; var n = d . Element ( "span" , { id : "MathJax_ZoomFrame" } , [ [ "span" , { id : "MathJax_ZoomOverlay" , onmousedown : this . Remove } ] , [ "span" , { id : "MathJax_Zoom" , onclick : this . Remove , style : { visibility : "hidden" , fontSize : this . settings . zscale } } , [ [ "span" , { style : { display : "inline-block" , "white-space" : "nowrap" } } ] ] ] ] ) ; var z = n . lastChild , w = z . firstChild , r = n . firstChild ; u . parentNode . insertBefore ( n , u ) ; u . parentNode . insertBefore ( u , n ) ; if ( w . addEventListener ) { w . addEventListener ( "mousedown" , this . Remove , true ) } var m = z . offsetWidth || z . clientWidth ; l -= m ; t -= m ; z . style . maxWidth = l + "px" ; z . style . maxHeight = t + "px" ; if ( this . msieTrapEventBug ) { var y = d . Element ( "span" , { id : "MathJax_ZoomEventTrap" , onmousedown : this . Remove } ) ; n . insertBefore ( y , z ) } if ( this . msieZIndexBug ) { var v = d . addElement ( document . body , "img" , { src : "about:blank" , id : "MathJax_ZoomTracker" , width : 0 , height : 0 , style : { width : 0 , height : 0 , position : "relative" } } ) ; n . style . position = "relative" ; n . style . zIndex = i . styles [ "#MathJax_ZoomOverlay" ] [ "z-index" ] ; n = v } var x = s . Zoom ( p , w , u , l , t ) ; if ( this . msiePositionBug ) { if ( this . msieSizeBug ) { z . style . height = x . zH + "px" ; z . style . width = x . zW + "px" } if ( z . offsetHeight > t ) { z . style . height = t + "px" ; z . style . width = ( x . zW + this . scrollSize ) + "px" } if ( z . offsetWidth > l ) { z . style . width = l + "px" ; z . style . height = ( x . zH + this . scrollSize ) + "px" } } if ( this . operaPositionBug ) { z . style . width = Math . min ( l , x . zW ) + "px" } if ( z . offsetWidth > m && z . offsetWidth - m < l && z . offsetHeight - m < t ) { z . style . overflow = "visible" } this . Position ( z , x ) ; if ( this . msieTrapEventBug ) { y . style . height = z . clientHeight + "px" ; y . style . width = z . clientWidth + "px" ; y . style . left = ( parseFloat ( z . style . left ) + z . clientLeft ) + "px" ; y . style . top = ( parse
( function ( f , n , p , e , q ) { var o = "2.6.1" ; var d = MathJax . Callback . Signal ( "menu" ) ; MathJax . Extension . MathMenu = { version : o , signal : d } ; var s = function ( t ) { return MathJax . Localization . _ . apply ( MathJax . Localization , [ [ "MathMenu" , t ] ] . concat ( [ ] . slice . call ( arguments , 1 ) ) ) } ; var a = f . Browser . isPC , k = f . Browser . isMSIE , l = ( ( document . documentMode || 0 ) > 8 ) ; var i = ( a ? null : "5px" ) ; var r = f . CombineConfig ( "MathMenu" , { delay : 150 , showRenderer : true , showMathPlayer : true , showFontMenu : false , showContext : false , showDiscoverable : false , showLocale : true , showLocaleURL : false , semanticsAnnotations : { TeX : [ "TeX" , "LaTeX" , "application/x-tex" ] , StarMath : [ "StarMath 5.0" ] , Maple : [ "Maple" ] , ContentMathML : [ "MathML-Content" , "application/mathml-content+xml" ] , OpenMath : [ "OpenMath" ] } , windowSettings : { status : "no" , toolbar : "no" , locationbar : "no" , menubar : "no" , directories : "no" , personalbar : "no" , resizable : "yes" , scrollbars : "yes" , width : 400 , height : 300 , left : Math . round ( ( screen . width - 400 ) / 2 ) , top : Math . round ( ( screen . height - 300 ) / 3 ) } , styles : { "#MathJax_About" : { position : "fixed" , left : "50%" , width : "auto" , "text-align" : "center" , border : "3px outset" , padding : "1em 2em" , "background-color" : "#DDDDDD" , color : "black" , cursor : "default" , "font-family" : "message-box" , "font-size" : "120%" , "font-style" : "normal" , "text-indent" : 0 , "text-transform" : "none" , "line-height" : "normal" , "letter-spacing" : "normal" , "word-spacing" : "normal" , "word-wrap" : "normal" , "white-space" : "nowrap" , "float" : "none" , "z-index" : 201 , "border-radius" : "15px" , "-webkit-border-radius" : "15px" , "-moz-border-radius" : "15px" , "-khtml-border-radius" : "15px" , "box-shadow" : "0px 10px 20px #808080" , "-webkit-box-shadow" : "0px 10px 20px #808080" , "-moz-box-shadow" : "0px 10px 20px #808080" , "-khtml-box-shadow" : "0px 10px 20px #808080" , filter : "progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')" } , "#MathJax_About.MathJax_MousePost" : { outline : "none" } , ".MathJax_Menu" : { position : "absolute" , "background-color" : "white" , color : "black" , width : "auto" , padding : ( a ? "2px" : "5px 0px" ) , border : "1px solid #CCCCCC" , margin : 0 , cursor : "default" , font : "menu" , "text-align" : "left" , "text-indent" : 0 , "text-transform" : "none" , "line-height" : "normal" , "letter-spacing" : "normal" , "word-spacing" : "normal" , "word-wrap" : "normal" , "white-space" : "nowrap" , "float" : "none" , "z-index" : 201 , "border-radius" : i , "-webkit-border-radius" : i , "-moz-border-radius" : i , "-khtml-border-radius" : i , "box-shadow" : "0px 10px 20px #808080" , "-webkit-box-shadow" : "0px 10px 20px #808080" , "-moz-box-shadow" : "0px 10px 20px #808080" , "-khtml-box-shadow" : "0px 10px 20px #808080" , filter : "progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')" } , ".MathJax_MenuItem" : { padding : ( a ? "2px 2em" : "1px 2em" ) , background : "transparent" } , ".MathJax_MenuArrow" : { position : "absolute" , right : ".5em" , "padding-top" : ".25em" , color : "#666666" , "font-family" : ( k ? "'Arial unicode MS'" : null ) , "font-size" : ".75em" } , ".MathJax_MenuActive .MathJax_MenuArrow" : { color : "white" } , ".MathJax_MenuArrow.RTL" : { left : ".5em" , right : "auto" } , ".MathJax_MenuCheck" : { position : "absolute" , left : ".7em" , "font-family" : ( k ? "'Arial unicode MS'" : null ) } , ".MathJax_MenuCheck.RTL" : { right : ".7em" , left : "auto" } , ".MathJax_MenuRadioCheck" : { position : "absolute" , left : ( a ? "1em" : ".7em" ) } , ".MathJax_MenuRadioCheck.RTL" : { right : ( a ? "1em" : ".7em" ) , left : "auto" } , ".MathJax_MenuLabel" : { padding : ( a ? "2px 2em 4px 1.33em" : "1px 2em 3px 1.33em" ) , "font-style" : "italic" } , ".MathJax_MenuRule" : { "border-top" : ( a ? "1px solid #CCCCCC" : "1px solid #DDDDDD" ) , margin : ( a ? "4px 1px 0px" : "4px 3px" ) } , ".MathJax_MenuDisabled" : { color : "GrayText" } , ".MathJax_MenuActive" : { "background-color" : ( a ? "Highlight" : "#606872" ) , color : ( a ? "HighlightText" : "white" ) } , ".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus" : { "background-color" : "#E8E8E8" } , ".MathJax_ContextMenu:focus" : { outline : "none" } , ".MathJax_ContextMenu .MathJax_MenuItem:focus" : { outline : "none" } , "#MathJax_AboutClose" : { top : ".2em" , right : ".2em" } , ".MathJax_Menu .MathJax_MenuClose" : { top : "-10px" , left : "-10px" } , ".MathJax_MenuClose" : { position : "absolute" , cursor : "pointer" , display : "inline-block" , border : "2px solid #AAA" , "border-radius" : "18px" , "-webkit-border-radius" : "18px" , "-moz-border-radius" : "18px" , "-khtml-border-radius" : " 18 px
MathJax . ElementJax . mml = MathJax . ElementJax ( { mimeType : "jax/mml" } , { id : "mml" , version : "2.6.0" , 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 . attr && this . root . attr . mode ) { if ( ! this . root . display && this . root . attr . mode === "display" ) { this . root . display = "block" ; this . root . attrNames . push ( "display" ) } delete this . root . attr . mode ; for ( var b = 0 , a = this . root . attrNames . length ; b < a ; b ++ ) { if ( this . root . attrNames [ b ] === "mode" ) { this . root . attrNames . splice ( b , 1 ) ; break } } } } } , { 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" , UPDIAGONALARROW : "updiagonalarrow" , VERTICALSTRIKE : "verticalstrike" , HORIZONTALSTRIKE : "horizontalstrike" , PHASORANGLE : "phasorangle" , 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 } , TEXCLASSNAMES : [ "ORD" , "OP" , "BIN" , "REL" , "OPEN" , "CLOSE" , "PUNCT" , "INNER" , "VCENTER" ] , skipAttributes : { texClass : true , useHeight : true , texprimestyle : true } , copyAttributes : { displaystyle : 1 , scriptlevel : 1 , open : 1 , close : 1 , form : 1 , actiontype : 1 , fontfamily : true , fontsize : true , fontweight : true , fontstyle : true , color : true , background : true , id : true , "class" : 1 , href : true , style : true } , copyAttributeNames : [ "displaystyle" , "scriptlevel" , "open" , "close" , "form" , "actiontype" , "fontfamily" , "fontsize" , "fontweight" , "fontstyle" , "color" , "background" , "id" , "class" , "href" , "style" ] , nocopyAttributes : { fontfamily : true , fontsize : true , fontweight : true , fontst
MathJax . Hub . Register . LoadHook ( "[MathJax]/jax/element/mml/jax.js" , function ( ) { var c = "2.6.1" ; var a = MathJax . ElementJax . mml , b = MathJax . Hub . config . menuSettings ; a . mbase . Augment ( { toMathML : function ( l ) { var h = ( this . inferred && this . parent . inferRow ) ; if ( l == null ) { l = "" } var f = this . type , e = this . toMathMLattributes ( ) ; if ( f === "mspace" ) { return l + "<" + f + e + " />" } var k = [ ] , j = ( this . isToken ? "" : l + ( h ? "" : " " ) ) ; for ( var g = 0 , d = this . data . length ; g < d ; g ++ ) { if ( this . data [ g ] ) { k . push ( this . data [ g ] . toMathML ( j ) ) } else { if ( ! this . isToken && ! this . isChars ) { k . push ( j + "<mrow />" ) } } } if ( this . isToken || this . isChars ) { return l + "<" + f + e + ">" + k . join ( "" ) + "</" + f + ">" } if ( h ) { return k . join ( "\n" ) } if ( k . length === 0 || ( k . length === 1 && k [ 0 ] === "" ) ) { return l + "<" + f + e + " />" } return l + "<" + f + e + ">\n" + k . join ( "\n" ) + "\n" + l + "</" + f + ">" } , toMathMLattributes : function ( ) { var j = ( this . type === "mstyle" ? a . math . prototype . defaults : this . defaults ) ; var h = ( this . attrNames || a . copyAttributeNames ) , g = a . skipAttributes , l = a . copyAttributes ; var e = [ ] ; if ( this . type === "math" && ( ! this . attr || ! this . attr . xmlns ) ) { e . push ( 'xmlns="http://www.w3.org/1998/Math/MathML"' ) } if ( ! this . attrNames ) { for ( var k in j ) { if ( ! g [ k ] && ! l [ k ] && j . hasOwnProperty ( k ) ) { if ( this [ k ] != null && this [ k ] !== j [ k ] ) { if ( this . Get ( k , null , 1 ) !== this [ k ] ) { e . push ( k + '="' + this . toMathMLattribute ( this [ k ] ) + '"' ) } } } } } for ( var f = 0 , d = h . length ; f < d ; f ++ ) { if ( l [ h [ f ] ] === 1 && ! j . hasOwnProperty ( h [ f ] ) ) { continue } value = ( this . attr || { } ) [ h [ f ] ] ; if ( value == null ) { value = this [ h [ f ] ] } if ( value != null ) { e . push ( h [ f ] + '="' + this . toMathMLquote ( value ) + '"' ) } } this . toMathMLclass ( e ) ; if ( e . length ) { return " " + e . join ( " " ) } else { return "" } } , toMathMLclass : function ( d ) { var f = [ ] ; if ( this [ "class" ] ) { f . push ( this [ "class" ] ) } if ( this . isa ( a . TeXAtom ) && b . texHints ) { var e = [ "ORD" , "OP" , "BIN" , "REL" , "OPEN" , "CLOSE" , "PUNCT" , "INNER" , "VCENTER" ] [ this . texClass ] ; if ( e ) { f . push ( "MJX-TeXAtom-" + e ) ; if ( e === "OP" && ! this . movablelimits ) { f . push ( "MJX-fixedlimits" ) } } } if ( this . mathvariant && this . toMathMLvariants [ this . mathvariant ] ) { f . push ( "MJX" + this . mathvariant ) } if ( this . variantForm ) { f . push ( "MJX-variant" ) } if ( f . length ) { d . unshift ( 'class="' + f . join ( " " ) + '"' ) } } , toMathMLattribute : function ( d ) { if ( typeof ( d ) === "string" && d . replace ( / /g , "" ) . match ( /^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/ ) ) { return ( RegExp . $2 || "" ) + ( ( 1 / 18 ) * RegExp . $3 ) . toFixed ( 3 ) . replace ( /\.?0+$/ , "" ) + "em" } else { if ( this . toMathMLvariants [ d ] ) { return this . toMathMLvariants [ d ] } } return this . toMathMLquote ( d ) } , toMathMLvariants : { "-tex-caligraphic" : a . VARIANT . SCRIPT , "-tex-caligraphic-bold" : a . VARIANT . BOLDSCRIPT , "-tex-oldstyle" : a . VARIANT . NORMAL , "-tex-oldstyle-bold" : a . VARIANT . BOLD , "-tex-mathit" : a . VARIANT . ITALIC } , toMathMLquote : function ( f ) { f = String ( f ) . split ( "" ) ; for ( var g = 0 , d = f . length ; g < d ; g ++ ) { var k = f [ g ] . charCodeAt ( 0 ) ; if ( k <= 55295 || 57344 <= k ) { if ( k > 126 || ( k < 32 && k !== 10 && k !== 13 && k !== 9 ) ) { f [ g ] = "&#x" + k . toString ( 16 ) . toUpperCase ( ) + ";" } else { var j = { "&" : "&" , "<" : "<" , ">" : ">" , '"' : """ } [ f [ g ] ] ; if ( j ) { f [ g ] = j } } } else { if ( g + 1 < d ) { var h = f [ g + 1 ] . charCodeAt ( 0 ) ; var e = ( ( ( k - 55296 ) << 10 ) + ( h - 56320 ) + 65536 ) ; f [ g ] = "&#x" + e . toString ( 16 ) . toUpperCase ( ) + ";" ; f [ g + 1 ] = "" ; g ++ } else { f [ g ] = "" } } } return f . join ( "" ) } } ) ; a . math . Augment ( { toMathML : function ( d , e ) { var g ; if ( d == null ) { d = "" } if ( e && e . originalText && b . semantics ) { g = MathJax . InputJax [ e . inputJax ] . annotationEncoding } var n = ( this . data [ 0 ] && this . data [ 0 ] . data . length > 1 ) ; var p = this . type , k = this . toMathMLattributes ( ) ; var j = [ ] , o = d + ( g ? " " + ( n ? " " : "" ) : "" ) + " " ; for ( var h = 0 , f = this . data . length ; h < f ; h ++ ) { if ( this . data [ h ] ) { j . push ( this . data [ h ] . toMathML ( o ) ) } else { j . push ( o + "<mrow />" ) } } if ( j . length === 0 || ( j . length === 1 && j [ 0 ] === "" ) ) { if ( ! g ) { return "<" + p + k + " />" } j . push ( o + "<mrow />" ) } if ( g ) { if ( n ) { j . unshift ( d + " <mrow>" ) ; j . push ( d + " </mrow>" ) } j . unshift ( d + " <semantics>" ) ; var l = e . originalText . replace ( /[&<>]/g , function ( i ) { return { ">" : ">" , "<" : "<" , "&" : "&" } [ i ] } ) ; j . push ( d + ' <annotation encoding="' + g + '">' + l + "</annotation>" ) ; j . push ( d + " </semantics>" ) } return d + "<" + p + k + ">\n" + j . join ( "\n" ) + "\n" + d + "</" + p + ">" } } ) ; a . msubsup . Augment ( { toMathML : function ( j ) { var f = this . type ; if ( this . data [ this . sup ] == null ) { f = "msub" } if ( this . data [ this . sub ] == null ) { f = "msup" } var e = this . toMathMLattributes ( ) ; delete this . data [ 0 ] . inferred ; var h = [ ] ; for ( var g = 0 , d = this . data . length ; g < d ; g ++ ) { if ( this . data [ g ] ) { h . push ( this . data [ g ] . toMathML ( j + " " ) ) }
( function ( c , d ) { var a ; var b = function ( e ) { return MathJax . Localization . _ . apply ( MathJax . Localization , [ [ "MathML" , e ] ] . concat ( [ ] . slice . call ( arguments , 1 ) ) ) } ; c . Parse = MathJax . Object . Subclass ( { Init : function ( f , e ) { this . Parse ( f , e ) } , Parse : function ( h , e ) { var j ; if ( typeof h !== "string" ) { j = h . parentNode } else { j = c . ParseXML ( this . preProcessMath . call ( this , h ) ) ; if ( j == null ) { c . Error ( [ "ErrorParsingMathML" , "Error parsing MathML" ] ) } } var g = j . getElementsByTagName ( "parsererror" ) [ 0 ] ; if ( g ) { c . Error ( [ "ParsingError" , "Error parsing MathML: %1" , g . textContent . replace ( /This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g , "" ) ] ) } if ( j . childNodes . length !== 1 ) { c . Error ( [ "MathMLSingleElement" , "MathML must be formed by a single element" ] ) } if ( j . firstChild . nodeName . toLowerCase ( ) === "html" ) { var f = j . getElementsByTagName ( "h1" ) [ 0 ] ; if ( f && f . textContent === "XML parsing error" && f . nextSibling ) { c . Error ( [ "ParsingError" , "Error parsing MathML: %1" , String ( f . nextSibling . nodeValue ) . replace ( /fatal parsing error: / , "" ) ] ) } } if ( j . firstChild . nodeName . toLowerCase ( ) . replace ( /^[a-z]+:/ , "" ) !== "math" ) { c . Error ( [ "MathMLRootElement" , "MathML must be formed by a <math> element, not %1" , "<" + j . firstChild . nodeName + ">" ] ) } var i = { math : j . firstChild , script : e } ; c . DOMfilterHooks . Execute ( i ) ; this . mml = this . MakeMML ( i . math ) } , MakeMML : function ( h ) { var i = String ( h . getAttribute ( "class" ) || "" ) ; var f , g = h . nodeName . toLowerCase ( ) . replace ( /^[a-z]+:/ , "" ) ; var e = ( i . match ( /(^| )MJX-TeXAtom-([^ ]*)/ ) ) ; if ( e ) { f = this . TeXAtom ( e [ 2 ] , e [ 2 ] === "OP" && ! i . match ( /MJX-fixedlimits/ ) ) } else { if ( ! ( a [ g ] && a [ g ] . isa && a [ g ] . isa ( a . mbase ) ) ) { MathJax . Hub . signal . Post ( [ "MathML Jax - unknown node type" , g ] ) ; return a . Error ( b ( "UnknownNodeType" , "Unknown node type: %1" , g ) ) } else { f = a [ g ] ( ) } } this . AddAttributes ( f , h ) ; this . CheckClass ( f , f [ "class" ] ) ; this . AddChildren ( f , h ) ; if ( c . config . useMathMLspacing ) { f . useMMLspacing = 8 } return f } , TeXAtom : function ( g , f ) { var e = a . TeXAtom ( ) . With ( { texClass : a . TEXCLASS [ g ] } ) ; if ( f ) { e . movesupsub = e . movablelimits = true } return e } , CheckClass : function ( f , h ) { h = ( h || "" ) . split ( / / ) ; var j = [ ] ; for ( var g = 0 , e = h . length ; g < e ; g ++ ) { if ( h [ g ] . substr ( 0 , 4 ) === "MJX-" ) { if ( h [ g ] === "MJX-arrow" ) { if ( ! f . notation . match ( "/" + a . NOTATION . UPDIAGONALARROW + "/" ) ) { f . notation += " " + a . NOTATION . UPDIAGONALARROW } } else { if ( h [ g ] === "MJX-variant" ) { f . variantForm = true ; if ( ! MathJax . Extension [ "TeX/AMSsymbols" ] ) { MathJax . Hub . RestartAfter ( MathJax . Ajax . Require ( "[MathJax]/extensions/TeX/AMSsymbols.js" ) ) } } else { if ( h [ g ] . substr ( 0 , 11 ) !== "MJX-TeXAtom" ) { f . mathvariant = h [ g ] . substr ( 3 ) ; if ( f . mathvariant === "-tex-caligraphic-bold" || f . mathvariant === "-tex-oldstyle-bold" ) { if ( ! MathJax . Extension [ "TeX/boldsymbol" ] ) { MathJax . Hub . RestartAfter ( MathJax . Ajax . Require ( "[MathJax]/extensions/TeX/boldsymbol.js" ) ) } } } } } } else { j . push ( h [ g ] ) } } if ( j . length ) { f [ "class" ] = j . join ( " " ) } else { delete f [ "class" ] } } , AddAttributes : function ( g , j ) { g . attr = { } ; g . attrNames = [ ] ; for ( var h = 0 , e = j . attributes . length ; h < e ; h ++ ) { var f = j . attributes [ h ] . name ; if ( f == "xlink:href" ) { f = "href" } if ( f . match ( /:/ ) ) { continue } if ( f . match ( /^_moz-math-((column|row)(align|line)|font-style)$/ ) ) { continue } var k = j . attributes [ h ] . value ; k = this . filterAttribute ( f , k ) ; var l = ( g . type === "mstyle" ? a . math . prototype . defaults : g . defaults ) ; if ( k != null ) { if ( k . toLowerCase ( ) === "true" ) { k = true } else { if ( k . toLowerCase ( ) === "false" ) { k = false } } if ( l [ f ] != null || a . copyAttributes [ f ] ) { g [ f ] = k } else { g . attr [ f ] = k } g . attrNames . push ( f ) } } } , filterAttribute : function ( e , f ) { return f } , AddChildren : function ( e , g ) { for ( var k = 0 , j = g . childNodes . length ; k < j ; k ++ ) { var f = g . childNodes [ k ] ; if ( f . nodeName === "#comment" ) { continue } if ( f . nodeName === "#text" ) { if ( ( e . isToken || e . isChars ) && ! e . mmlSelfClosing ) { var o = f . nodeValue ; if ( e . isToken ) { o = o . replace ( /&([a-z][a-z0-9]*);/ig , this . replaceEntity ) ; o = this . trimSpace ( o ) } e . Append ( a . chars ( o ) ) } else { if ( f . nodeValue . match ( /\S/ ) ) { c . Error ( [ "UnexpectedTextNode" , "Unexpected text node: %1" , "'" + f . nodeValue + "'" ] ) } } } else { if ( e . type === "annotation-xml" ) { e . Append ( a . xml ( f ) ) } else { var h = this . MakeMML ( f ) ; e . Append ( h ) ; if ( h . mmlSelfClosing && h . data . length ) { e . Append . apply ( e , h . data ) ; h . data = [ ] } } } } if ( e . type === "mrow" && e . data . length >= 2 ) { var l = e . data [ 0 ] , n = e . data [ e . data . length - 1 ] ; if ( l . type === "mo" && l . Get ( "fence" ) && n . type === "mo" && n . Get ( "fence" ) ) { if ( l . data [ 0 ] ) { e . open = l . data . joi
( function ( l , c , g , e ) { var f , i = c . Browser . isMSIE ; var h , b , d , k ; c . Register . StartupHook ( "MathZoom Ready" , function ( ) { k = MathJax . Extension . MathZoom } ) ; var j = function ( m , o ) { var n = e . Element ( "span" ) ; m = "padding" + m ; if ( o ) { n . style . cssText = ( o . getAttribute ( "style" ) || "" ) ; if ( n . style . padding === "" && ( n . style [ m ] || "" ) === "" ) { n . style [ m ] = "0px" ; o . setAttribute ( "style" , n . style . cssText ) } } } ; var a = function ( r , m , p ) { if ( r ) { var o = e . Element ( "span" ) ; o . style . cssText = ( r . getAttribute ( "style" ) || "" ) ; if ( o . style . padding === "" ) { var q = { paddingLeft : p , paddingTop : m , paddingRight : "0px" , paddingBottom : "0px" } ; for ( var n in q ) { if ( q . hasOwnProperty ( n ) ) { if ( ( o . style [ n ] || "" ) === "" ) { o . style [ n ] = q [ n ] } } } } r . setAttribute ( "style" , o . style . cssText ) } } ; l . Augment ( { config : { styles : { ".MathJax_MathML" : { "font-style" : "normal" , "font-weight" : "normal" , "line-height" : "normal" , "font-size" : "100%" , "font-size-adjust" : "none" , "text-indent" : 0 , "text-align" : "left" , "text-transform" : "none" , "letter-spacing" : "normal" , "word-spacing" : "normal" , "word-wrap" : "normal" , "white-space" : "nowrap" , "float" : "none" , direction : "ltr" , "max-width" : "none" , "max-height" : "none" , "min-width" : 0 , "min-height" : 0 , border : 0 , padding : 0 , margin : 0 } , "span.MathJax_MathML" : { display : "inline!important" } , "div.MathJax_MathML" : { display : "block!important" } , ".MathJax_mmlExBox" : { display : "block!important" , overflow : "hidden" , height : "1px" , width : "60ex" , "min-height" : 0 , "max-height" : "none" , padding : 0 , border : 0 , margin : 0 } } } , handlesVariants : false , settings : c . config . menuSettings , ex : 1 , scale : 1 , adjustWidths : [ ] , Config : function ( ) { this . SUPER ( arguments ) . Config . call ( this ) ; if ( this . settings . scale ) { this . config . scale = this . settings . scale } if ( c . config . displayAlign !== "center" ) { var o = c . config . displayAlign , m = c . config . displayIndent ; var n = { "text-align" : o + "!important" } ; n [ "margin-" + o ] = m + "!important" ; c . Insert ( this . config . styles , { "div.MathJax_MathML" : n , "div.MathJax_MathML math" : { "text-align" : o } , "div.MathJax_MathContainer > span" : { "text-align" : o + "!important" } } ) } if ( ! this . require ) { this . require = [ ] } this . require . push ( MathJax . OutputJax . extensionDir + "/MathEvents.js" ) } , Startup : function ( ) { h = MathJax . Extension . MathEvents . Event ; b = MathJax . Extension . MathEvents . Touch ; d = MathJax . Extension . MathEvents . Hover ; this . ContextMenu = h . ContextMenu ; this . Mousedown = h . AltContextMenu ; this . Mouseover = d . Mouseover ; this . Mouseout = d . Mouseout ; this . Mousemove = d . Mousemove ; if ( ! c . Browser . hasMathPlayer ) { this . EmExSpan = e . Element ( "span" , { style : { position : "absolute" , "font-size-adjust" : "none" } } , [ [ "div" , { className : "MathJax_mmlExBox" } ] , [ "span" , { className : "MathJax_MathML" } ] ] ) ; f . math ( f . mspace ( ) . With ( { width : "60ex" } ) ) . toNativeMML ( this . EmExSpan . lastChild ) } return g . Styles ( this . config . styles ) } , InitializeMML : function ( ) { this . initialized = true ; if ( c . Browser . hasMathPlayer ) { try { if ( ! c . Browser . mpNamespace ) { var m = document . createElement ( "object" ) ; m . id = "mathplayer" ; m . classid = "clsid:32F66A20-7614-11D4-BD11-00104BD3F987" ; document . getElementsByTagName ( "head" ) [ 0 ] . appendChild ( m ) ; document . namespaces . add ( "m" , "http://www.w3.org/1998/Math/MathML" ) ; c . Browser . mpNamespace = true } if ( ! c . Browser . mpImported ) { document . namespaces . m . doImport ( "#mathplayer" ) ; c . Browser . mpImported = true } } catch ( n ) { if ( ! this . config . noMathPlayerWarning ) { alert ( MathJax . Localization . _ ( [ "MathML" , "MathPlayer" ] , "MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX \ncontrols from running. Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics." ) ) } } } else { document . body . appendChild ( this . EmExSpan ) ; this . defaultEx = this . EmExSpan . firstChild . offsetWidth / 60 ; this . defaultMEx = this . EmExSpan . lastChild . offsetWidth / 60 ; document . body . removeChild ( this . EmExSpan ) } } , preTranslate : function ( o ) { var t = o . jax [ this . id ] , u , p = t . length , y , r , A , w , z , n , v , s , q ; for ( u = 0 ; u < p ; u ++ ) { y = t [ u ] ; if ( ! y . parentNode ) { continue } if ( ! this . initialized ) { this . InitializeMML ( ) } r = y . previousSibling ; if ( r && r . className === "MathJax_MathML" ) { r . parentNode . removeCh
( function ( h , b , d ) { var g , i = b . Browser . isMobile ; var e = function ( ) { var k = [ ] . slice . call ( arguments , 0 ) ; k [ 0 ] [ 0 ] = [ "HTML-CSS" , k [ 0 ] [ 0 ] ] ; return MathJax . Message . Set . apply ( MathJax . Message , k ) } ; var f = MathJax . Object . Subclass ( { timeout : ( i ? 15 : 8 ) * 1000 , comparisonFont : [ "sans-serif" , "monospace" , "script" , "Times" , "Courier" , "Arial" , "Helvetica" ] , testSize : [ "40px" , "50px" , "60px" , "30px" , "20px" ] , FedoraSTIXcheck : { family : "STIXSizeOneSym" , testString : "abcABC" , noStyleChar : true } , Init : function ( ) { this . div = MathJax . HTML . addElement ( document . body , "div" , { style : { position : "absolute" , width : 0 , height : 0 , overflow : "hidden" , padding : 0 , border : 0 , margin : 0 } } , [ [ "div" , { id : "MathJax_Font_Test" , style : { position : "absolute" , visibility : "hidden" , top : 0 , left : 0 , width : "auto" , padding : 0 , border : 0 , margin : 0 , whiteSpace : "nowrap" , textAlign : "left" , textIndent : 0 , textTransform : "none" , lineHeight : "normal" , letterSpacing : "normal" , wordSpacing : "normal" , fontSize : this . testSize [ 0 ] , fontWeight : "normal" , fontStyle : "normal" , fontSizeAdjust : "none" } } , [ "" ] ] ] ) . firstChild ; this . text = this . div . firstChild } , findFont : function ( p , l ) { var o = null ; if ( l && this . testCollection ( l ) ) { o = l } else { for ( var n = 0 , k = p . length ; n < k ; n ++ ) { if ( p [ n ] === l ) { continue } if ( this . testCollection ( p [ n ] ) ) { o = p [ n ] ; break } } } if ( o === "STIX" && this . testFont ( this . FedoraSTIXcheck ) ) { o = null } return o } , testCollection : function ( l ) { var k = { testString : "() {} []" } ; k . family = { TeX : "MathJax_Size1" , STIX : "STIXSizeOneSym" } [ l ] || l . replace ( /-(Math)?/ , "" ) + "MathJax_Size1" ; if ( l === "STIX" ) { k . noStyleChar = true } return this . testFont ( k ) } , testFont : function ( n ) { if ( n . isWebFont && d . FontFaceBug ) { this . div . style . fontWeight = this . div . style . fontStyle = "normal" } else { this . div . style . fontWeight = ( n . weight || "normal" ) ; this . div . style . fontStyle = ( n . style || "normal" ) } var p = n . familyFixed || n . family ; if ( ! n . isWebFont && ! p . match ( /^(STIX|MathJax)|'/ ) ) { p = p . replace ( /_/g , " " ) . replace ( /([a-z])([A-Z])/g , "$1 $2" ) . replace ( / Jax/ , "Jax" ) + "','" + p + "','" + p + "-" ; if ( n . weight ) { p += "Bold" } if ( n . style ) { p += "Italic" } if ( ! n . weight && ! n . style ) { p += "Regular" } n . familyFixed = p = "'" + p + "'" } var l = this . getComparisonWidths ( n . testString , n . noStyleChar ) ; var q = null ; if ( l ) { this . div . style . fontFamily = p + "," + this . comparisonFont [ 0 ] ; if ( this . div . offsetWidth == l [ 0 ] ) { this . div . style . fontFamily = p + "," + this . comparisonFont [ l [ 2 ] ] ; if ( this . div . offsetWidth == l [ 1 ] ) { q = false } } if ( q === null && ( this . div . offsetWidth != l [ 3 ] || this . div . offsetHeight != l [ 4 ] ) ) { if ( ! n . noStyleChar && d . FONTDATA && d . FONTDATA . hasStyleChar ) { for ( var o = 0 , k = this . testSize . length ; o < k ; o ++ ) { if ( this . testStyleChar ( n , this . testSize [ o ] ) ) { q = true ; k = 0 } } } else { q = true } } } if ( d . safariTextNodeBug ) { this . div . innerHTML = "" } else { this . text . nodeValue = "" } return q } , styleChar : "\uEFFD" , versionChar : "\uEFFE" , compChar : "\uEFFF" , testStyleChar : function ( m , p ) { var s = 3 + ( m . weight ? 2 : 0 ) + ( m . style ? 4 : 0 ) ; var l = "" , o = 0 ; var r = this . div . style . fontSize ; this . div . style . fontSize = p ; if ( d . msieItalicWidthBug && m . style === "italic" ) { this . text . nodeValue = l = this . compChar ; o = this . div . offsetWidth } if ( d . safariTextNodeBug ) { this . div . innerHTML = this . compChar + l } else { this . text . nodeValue = this . compChar + l } var k = this . div . offsetWidth - o ; if ( d . safariTextNodeBug ) { this . div . innerHTML = this . styleChar + l } else { this . text . nodeValue = this . styleChar + l } var q = Math . floor ( ( this . div . offsetWidth - o ) / k + 0.5 ) ; if ( q === s ) { if ( d . safariTextNodeBug ) { this . div . innerHTML = this . versionChar + l } else { this . text . nodeValue = this . versionChar + l } m . version = Math . floor ( ( this . div . offsetWidth - o ) / k + 1.5 ) / 2 } this . div . style . fontSize = r ; return ( q === s ) } , getComparisonWidths : function ( p , n ) { if ( d . FONTDATA && d . FONTDATA . hasStyleChar && ! n ) { p += this . styleChar + " " + this . compChar } if ( d . safariTextNodeBug ) { this . div . innerHTML = p } else { this . text . nodeValue = p } this . div . style . fontFamily = this . comparisonFont [ 0 ] ; var l = this . div . offsetWidth ; this . div . style . fontFamily = d . webFontDefault ; var r = this . div . offsetWidth , o = this . div . offsetHeight ; for ( var q = 1 , k = this . comparisonFont . length ; q < k ; q ++ ) { this . div . style . fontFamily = this . comparisonFont [ q ] ; if ( this . div . offsetWidth != l ) { return [ l , this . div . offsetWidth , q , r , o ] } } return null } , loadWebFont : function ( l ) { b . Startup . signal . Post ( "HTML-CSS Jax - Web-Font " + d . fontInUse + "/" + l . directory ) ; var o = e ( [ "LoadWebFont" , "Loading web-font %1" , d . fontInUse + "/" + l . directory ] ) ; var k = MathJax . Callback ( { } ) ; var m = MathJax . Callba
MathJax . Hub . Register . StartupHook ( "HTML-CSS Jax Ready" , function ( ) { var c = "2.6.0" ; var a = MathJax . ElementJax . mml , b = MathJax . OutputJax [ "HTML-CSS" ] ; a . mtable . Augment ( { toHTML : function ( r ) { r = this . HTMLcreateSpan ( r ) ; if ( this . data . length === 0 ) { return r } var I = this . getValues ( "columnalign" , "rowalign" , "columnspacing" , "rowspacing" , "columnwidth" , "equalcolumns" , "equalrows" , "columnlines" , "rowlines" , "frame" , "framespacing" , "align" , "useHeight" , "width" , "side" , "minlabelspacing" ) ; var aM = I . width . match ( /%$/ ) ; var ay = b . createStack ( r ) ; var aJ = this . HTMLgetScale ( ) , aB = this . HTMLgetMu ( r ) , aC = - 1 ; var aq = [ ] , au = [ ] , aj = [ ] , aw = [ ] , av = [ ] , ae , ad , ap = - 1 , ac , ao , X , aH , Q , aE , aR = [ ] , aW ; var G = b . FONTDATA . lineH * aJ * I . useHeight , N = b . FONTDATA . lineD * aJ * I . useHeight ; for ( ae = 0 , ac = this . data . length ; ae < ac ; ae ++ ) { aH = this . data [ ae ] ; X = ( aH . type === "mlabeledtr" ? aC : 0 ) ; aw [ ae ] = [ ] ; aq [ ae ] = G ; au [ ae ] = N ; for ( ad = X , ao = aH . data . length + X ; ad < ao ; ad ++ ) { if ( aj [ ad ] == null ) { if ( ad > ap ) { ap = ad } av [ ad ] = b . createStack ( b . createBox ( ay ) ) ; aj [ ad ] = - b . BIGDIMEN } aw [ ae ] [ ad ] = b . createBox ( av [ ad ] ) ; aR . push ( aH . data [ ad - X ] . toHTML ( aw [ ae ] [ ad ] ) ) } } b . MeasureSpans ( aR ) ; for ( ae = 0 , ac = this . data . length ; ae < ac ; ae ++ ) { aH = this . data [ ae ] ; X = ( aH . type === "mlabeledtr" ? aC : 0 ) ; for ( ad = X , ao = aH . data . length + X ; ad < ao ; ad ++ ) { Q = aH . data [ ad - X ] ; if ( Q . isMultiline ) { aw [ ae ] [ ad ] . style . width = "100%" } if ( Q . isEmbellished ( ) ) { aE = Q . CoreMO ( ) ; var aV = aE . Get ( "minsize" , true ) ; if ( aV ) { var aO = aE . HTMLspanElement ( ) . bbox ; if ( aE . HTMLcanStretch ( "Vertical" ) ) { aW = aO . h + aO . d ; if ( aW ) { aV = b . length2em ( aV , aB , aW ) ; if ( aV * aO . h / aW > aq [ ae ] ) { aq [ ae ] = aV * aO . h / aW } if ( aV * aO . d / aW > au [ ae ] ) { au [ ae ] = aV * aO . d / aW } } } else { if ( aE . HTMLcanStretch ( "Horizontal" ) ) { aV = b . length2em ( aV , aB , aO . w ) ; if ( aV > aj [ ad ] ) { aj [ ad ] = aV } } } } } if ( aw [ ae ] [ ad ] . bbox . h > aq [ ae ] ) { aq [ ae ] = aw [ ae ] [ ad ] . bbox . h } if ( aw [ ae ] [ ad ] . bbox . d > au [ ae ] ) { au [ ae ] = aw [ ae ] [ ad ] . bbox . d } if ( aw [ ae ] [ ad ] . bbox . w > aj [ ad ] ) { aj [ ad ] = aw [ ae ] [ ad ] . bbox . w } } } var aG = MathJax . Hub . SplitList ; var aA = aG ( I . columnspacing ) , aT = aG ( I . rowspacing ) , e = aG ( I . columnalign ) , B = aG ( I . rowalign ) , d = aG ( I . columnlines ) , w = aG ( I . rowlines ) , aP = aG ( I . columnwidth ) , U = [ ] ; for ( ae = 0 , ac = aA . length ; ae < ac ; ae ++ ) { aA [ ae ] = b . length2em ( aA [ ae ] , aB ) } for ( ae = 0 , ac = aT . length ; ae < ac ; ae ++ ) { aT [ ae ] = b . length2em ( aT [ ae ] , aB ) } while ( aA . length < ap ) { aA . push ( aA [ aA . length - 1 ] ) } while ( e . length <= ap ) { e . push ( e [ e . length - 1 ] ) } while ( d . length < ap ) { d . push ( d [ d . length - 1 ] ) } while ( aP . length <= ap ) { aP . push ( aP [ aP . length - 1 ] ) } while ( aT . length < aw . length ) { aT . push ( aT [ aT . length - 1 ] ) } while ( B . length <= aw . length ) { B . push ( B [ B . length - 1 ] ) } while ( w . length < aw . length ) { w . push ( w [ w . length - 1 ] ) } if ( av [ aC ] ) { e [ aC ] = ( I . side . substr ( 0 , 1 ) === "l" ? "left" : "right" ) ; aA [ aC ] = - aj [ aC ] } for ( ae = 0 , ac = aw . length ; ae < ac ; ae ++ ) { aH = this . data [ ae ] ; U [ ae ] = [ ] ; if ( aH . rowalign ) { B [ ae ] = aH . rowalign } if ( aH . columnalign ) { U [ ae ] = aG ( aH . columnalign ) ; while ( U [ ae ] . length <= ap ) { U [ ae ] . push ( U [ ae ] [ U [ ae ] . length - 1 ] ) } } } if ( I . equalrows ) { var aF = Math . max . apply ( Math , aq ) , V = Math . max . apply ( Math , au ) ; for ( ae = 0 , ac = aw . length ; ae < ac ; ae ++ ) { X = ( ( aF + V ) - ( aq [ ae ] + au [ ae ] ) ) / 2 ; aq [ ae ] += X ; au [ ae ] += X } } aW = aq [ 0 ] + au [ aw . length - 1 ] ; for ( ae = 0 , ac = aw . length - 1 ; ae < ac ; ae ++ ) { aW += Math . max ( 0 , au [ ae ] + aq [ ae + 1 ] + aT [ ae ] ) } var aL = 0 , aK = 0 , aZ , g = aW ; if ( I . frame !== "none" || ( I . columnlines + I . rowlines ) . match ( /solid|dashed/ ) ) { var v = aG ( I . framespacing ) ; if ( v . length != 2 ) { v = aG ( this . defaults . framespacing ) } aL = b . length2em ( v [ 0 ] , aB ) ; aK = b . length2em ( v [ 1 ] , aB ) ; g = aW + 2 * aK } var ai , aY , aa = "" ; if ( typeof ( I . align ) !== "string" ) { I . align = String ( I . align ) } if ( I . align . match ( /(top|bottom|center|baseline|axis)( +(-?\d+))?/ ) ) { aa = RegExp . $3 || "" ; I . align = RegExp . $1 } else { I . align = this . defaults . align } if ( aa !== "" ) { aa = parseInt ( aa ) ; if ( aa < 0 ) { aa = aw . length + 1 + aa } if ( aa < 1 ) { aa = 1 } else { if ( aa > aw . length ) { aa = aw . length } } ai = 0 ; aY = - ( aW + aK ) + aq [ 0 ] ; for ( ae = 0 , ac = aa - 1 ; ae < ac ; ae ++ ) { var L = Math . max ( 0 , au [ ae ] + aq [ ae + 1 ] + aT [ ae ] ) ; ai += L ; aY += L } } else { ai = ( { top : - ( aq [ 0 ] + aK ) , bottom : aW + aK - aq [ 0 ] , center : aW / 2 - aq [ 0 ] , baseline : aW / 2 - aq [ 0 ] , axis : aW / 2 + b . TeX . axis _height * aJ - aq [ 0 ] } ) [ I . align ] ; aY = ( { top : - ( aW + 2 * aK ) , bottom : 0 , center : - ( aW / 2 + aK ) , baseline : - ( aW / 2 + aK ) , axis : b . TeX . axis _height * aJ - aW / 2 - aK } ) [ I . align ] } var ab , af = 0 , z = 0 , K = 0 , Z = 0 , ag = 0 , am = [ ] , at = [ ] , R = 1 ; if ( I . equalcolumns && I . width !== "auto" ) { if ( aM ) { ab = ( 100 / ( ap + 1 ) ) . toFixed ( 2 ) . replace ( /\.?0+$/ , "" ) + "%" ; for ( ae = 0 , ac = Math . min ( ap + 1 , aP . length ) ; ae < ac ; ae ++ ) { aP [ ae ] = ab } ab = 0 ; af = 1 ; ag = ap + 1 ; for ( ae = 0 , ac = Math . min ( ap + 1 , aA . length ) ; ae < ac ; ae ++ ) { ab += aA [ ae ] } } else { ab = b
( function ( i , b , e , g ) { var h ; var j , a , d ; var f = "'Times New Roman',Times,STIXGeneral,serif" ; var m = { ".MJXp-script" : { "font-size" : ".8em" } , ".MJXp-right" : { "-webkit-transform-origin" : "right" , "-moz-transform-origin" : "right" , "-ms-transform-origin" : "right" , "-o-transform-origin" : "right" , "transform-origin" : "right" } , ".MJXp-bold" : { "font-weight" : "bold" } , ".MJXp-italic" : { "font-style" : "italic" } , ".MJXp-scr" : { "font-family" : "MathJax_Script," + f } , ".MJXp-frak" : { "font-family" : "MathJax_Fraktur," + f } , ".MJXp-sf" : { "font-family" : "MathJax_SansSerif," + f } , ".MJXp-cal" : { "font-family" : "MathJax_Caligraphic," + f } , ".MJXp-mono" : { "font-family" : "MathJax_Typewriter," + f } , ".MJXp-largeop" : { "font-size" : "150%" } , ".MJXp-largeop.MJXp-int" : { "vertical-align" : "-.2em" } , ".MJXp-math" : { display : "inline-block" , "line-height" : "1.2" , "text-indent" : "0" , "font-family" : f , "white-space" : "nowrap" , "border-collapse" : "collapse" } , ".MJXp-display" : { display : "block" , "text-align" : "center" , margin : "1em 0" } , ".MJXp-math span" : { display : "inline-block" } , ".MJXp-box" : { display : "block!important" , "text-align" : "center" } , ".MJXp-box:after" : { content : '" "' } , ".MJXp-rule" : { display : "block!important" , "margin-top" : ".1em" } , ".MJXp-char" : { display : "block!important" } , ".MJXp-mo" : { margin : "0 .15em" } , ".MJXp-mfrac" : { margin : "0 .125em" , "vertical-align" : ".25em" } , ".MJXp-denom" : { display : "inline-table!important" , width : "100%" } , ".MJXp-denom > *" : { display : "table-row!important" } , ".MJXp-surd" : { "vertical-align" : "top" } , ".MJXp-surd > *" : { display : "block!important" } , ".MJXp-script-box > * " : { display : "table!important" , height : "50%" } , ".MJXp-script-box > * > *" : { display : "table-cell!important" , "vertical-align" : "top" } , ".MJXp-script-box > *:last-child > *" : { "vertical-align" : "bottom" } , ".MJXp-script-box > * > * > *" : { display : "block!important" } , ".MJXp-mphantom" : { visibility : "hidden" } , ".MJXp-munderover" : { display : "inline-table!important" } , ".MJXp-over" : { display : "inline-block!important" , "text-align" : "center" } , ".MJXp-over > *" : { display : "block!important" } , ".MJXp-munderover > *" : { display : "table-row!important" } , ".MJXp-mtable" : { "vertical-align" : ".25em" , margin : "0 .125em" } , ".MJXp-mtable > *" : { display : "inline-table!important" , "vertical-align" : "middle" } , ".MJXp-mtr" : { display : "table-row!important" } , ".MJXp-mtd" : { display : "table-cell!important" , "text-align" : "center" , padding : ".5em 0 0 .5em" } , ".MJXp-mtr > .MJXp-mtd:first-child" : { "padding-left" : 0 } , ".MJXp-mtr:first-child > .MJXp-mtd" : { "padding-top" : 0 } , ".MJXp-mlabeledtr" : { display : "table-row!important" } , ".MJXp-mlabeledtr > .MJXp-mtd:first-child" : { "padding-left" : 0 } , ".MJXp-mlabeledtr:first-child > .MJXp-mtd" : { "padding-top" : 0 } , ".MJXp-merror" : { "background-color" : "#FFFF88" , color : "#CC0000" , border : "1px solid #CC0000" , padding : "1px 3px" , "font-style" : "normal" , "font-size" : "90%" } } ; ( function ( ) { for ( var n = 0 ; n < 10 ; n ++ ) { var o = "scaleX(." + n + ")" ; m [ ".MJXp-scale" + n ] = { "-webkit-transform" : o , "-moz-transform" : o , "-ms-transform" : o , "-o-transform" : o , transform : o } } } ) ( ) ; var k = 1000000 ; var c = "V" , l = "H" ; g . Augment ( { settings : b . config . menuSettings , config : { styles : m } , hideProcessedMath : false , maxStretchyParts : 1000 , Config : function ( ) { if ( ! this . require ) { this . require = [ ] } this . SUPER ( arguments ) . Config . call ( this ) ; var n = this . settings ; if ( n . scale ) { this . config . scale = n . scale } this . require . push ( MathJax . OutputJax . extensionDir + "/MathEvents.js" ) } , Startup : function ( ) { j = MathJax . Extension . MathEvents . Event ; a = MathJax . Extension . MathEvents . Touch ; d = MathJax . Extension . MathEvents . Hover ; this . ContextMenu = j . ContextMenu ; this . Mousedown = j . AltContextMenu ; this . Mouseover = d . Mouseover ; this . Mouseout = d . Mouseout ; this . Mousemove = d . Mousemove ; var n = e . addElement ( document . body , "div" , { style : { width : "5in" } } ) ; this . pxPerInch = n . offsetWidth / 5 ; n . parentNode . removeChild ( n ) ; return i . Styles ( this . config . styles , [ "InitializePHTML" , this ] ) } , InitializePHTML : function ( ) { } , preTranslate : function ( p ) { var s = p . jax [ this . id ] , t , q = s . length , u , r , v , o , n ; for ( t = 0 ; t < q ; t ++ ) { u = s [ t ] ; if ( ! u . parentNode ) { continue } r = u . previousSibling ; if ( r && String ( r . className ) . match ( /^MathJax_PHTML(_Display)?( MathJax_Processing)?$/ ) ) { r . parentNode . removeChild ( r ) } n = u . MathJax . elementJax ; if ( ! n ) { continue } n . PHTML = { display : ( n . root . Get ( "display" ) === "block" ) } ; v = o = e . Element ( "span" , { className : " MathJax _PH
( function ( b , g , f ) { var c = b . config . menuSettings ; var e = MathJax . OutputJax ; var a = f . isMSIE && ( document . documentMode || 0 ) < 8 ; var d = MathJax . Extension [ "fast-preview" ] = { version : "2.6.0" , enabled : true , config : b . CombineConfig ( "fast-preview" , { Chunks : { EqnChunk : 10000 , EqnChunkFactor : 1 , EqnChunkDelay : 0 } , color : "inherit!important" , updateTime : 30 , updateDelay : 6 , messageStyle : "none" , disabled : f . isMSIE && ! f . versionAtLeast ( "8.0" ) } ) , Config : function ( ) { if ( b . config [ "CHTML-preview" ] ) { MathJax . Hub . Config ( { "fast-preview" : b . config [ "CHTML-preview" ] } ) } var m , j , k , h , l ; var i = this . config ; if ( ! i . disabled && c . FastPreview == null ) { b . Config ( { menuSettings : { FastPreview : true } } ) } if ( c . FastPreview ) { MathJax . Ajax . Styles ( { ".MathJax_Preview .MJXf-math" : { color : i . color } } ) ; b . Config ( { "HTML-CSS" : i . Chunks , CommonHTML : i . Chunks , SVG : i . Chunks } ) } b . Register . MessageHook ( "Begin Math Output" , function ( ) { if ( ! h && d . Active ( ) ) { m = b . processUpdateTime ; j = b . processUpdateDelay ; k = b . config . messageStyle ; b . processUpdateTime = i . updateTime ; b . processUpdateDelay = i . updateDelay ; b . Config ( { messageStyle : i . messageStyle } ) ; MathJax . Message . Clear ( 0 , 0 ) ; l = true } } ) ; b . Register . MessageHook ( "End Math Output" , function ( ) { if ( ! h && l ) { b . processUpdateTime = m ; b . processUpdateDelay = j ; b . Config ( { messageStyle : k } ) ; h = true } } ) } , Disable : function ( ) { this . enabled = false } , Enable : function ( ) { this . enabled = true } , Active : function ( ) { return c . FastPreview && this . enabled && ! ( e [ c . renderer ] || { } ) . noFastPreview } , Preview : function ( h ) { if ( ! this . Active ( ) ) { return } var i = h . script . MathJax . preview || h . script . previousSibling ; if ( ! i || i . className !== MathJax . Hub . config . preRemoveClass ) { i = g . Element ( "span" , { className : MathJax . Hub . config . preRemoveClass } ) ; h . script . parentNode . insertBefore ( i , h . script ) ; h . script . MathJax . preview = i } i . innerHTML = "" ; i . style . color = ( a ? "black" : "inherit" ) ; return this . postFilter ( i , h ) } , postFilter : function ( j , i ) { if ( ! i . math . root . toPreviewHTML ) { var h = MathJax . Callback . Queue ( ) ; h . Push ( [ "Require" , MathJax . Ajax , "[MathJax]/jax/output/PreviewHTML/config.js" ] , [ "Require" , MathJax . Ajax , "[MathJax]/jax/output/PreviewHTML/jax.js" ] ) ; b . RestartAfter ( h . Push ( { } ) ) } i . math . root . toPreviewHTML ( j ) } , Register : function ( h ) { b . Register . StartupHook ( h + " Jax Require" , function ( ) { var i = MathJax . InputJax [ h ] ; i . postfilterHooks . Add ( [ "Preview" , MathJax . Extension [ "fast-preview" ] ] , 50 ) } ) } } ; d . Register ( "TeX" ) ; d . Register ( "MathML" ) ; d . Register ( "AsciiMath" ) ; b . Register . StartupHook ( "End Config" , [ "Config" , d ] ) ; b . Startup . signal . Post ( "fast-preview Ready" ) } ) ( MathJax . Hub , MathJax . HTML , MathJax . Hub . Browser ) ; MathJax . Ajax . loadComplete ( "[MathJax]/extensions/fast-preview.js" ) ;
( function ( a , e , b , f ) { var c = b . config . menuSettings ; var d = MathJax . Extension . AssistiveMML = { version : "2.6.1" , config : b . CombineConfig ( "AssistiveMML" , { disabled : false , styles : { ".MJX_Assistive_MathML" : { position : "absolute!important" , top : 0 , left : 0 , clip : ( b . Browser . isMSIE && ( document . documentMode || 0 ) < 8 ? "rect(1px 1px 1px 1px)" : "rect(1px, 1px, 1px, 1px)" ) , padding : "1px 0 0 0!important" , border : "0!important" , height : "1px!important" , width : "1px!important" , overflow : "hidden!important" , display : "block!important" , "-webkit-touch-callout" : "none" , "-webkit-user-select" : "none" , "-khtml-user-select" : "none" , "-moz-user-select" : "none" , "-ms-user-select" : "none" , "user-select" : "none" } , ".MJX_Assistive_MathML.MJX_Assistive_MathML_Block" : { width : "100%!important" } } } ) , Config : function ( ) { if ( ! this . config . disabled && c . assistiveMML == null ) { b . Config ( { menuSettings : { assistiveMML : true } } ) } a . Styles ( this . config . styles ) ; b . Register . MessageHook ( "End Math" , function ( g ) { if ( c . assistiveMML ) { return d . AddAssistiveMathML ( g [ 1 ] ) } } ) } , AddAssistiveMathML : function ( g ) { var h = { jax : b . getAllJax ( g ) , i : 0 , callback : MathJax . Callback ( { } ) } ; this . HandleMML ( h ) ; return h . callback } , RemoveAssistiveMathML : function ( k ) { var h = b . getAllJax ( k ) , l ; for ( var j = 0 , g = h . length ; j < g ; j ++ ) { l = document . getElementById ( h [ j ] . inputID + "-Frame" ) ; if ( l && l . getAttribute ( "data-mathml" ) ) { l . removeAttribute ( "data-mathml" ) ; if ( l . lastChild && l . lastChild . className . match ( /MJX_Assistive_MathML/ ) ) { l . removeChild ( l . lastChild ) } } } } , HandleMML : function ( l ) { var g = l . jax . length , h , i , n , j ; while ( l . i < g ) { h = l . jax [ l . i ] ; n = document . getElementById ( h . inputID + "-Frame" ) ; if ( h . outputJax !== "NativeMML" && n && ! n . getAttribute ( "data-mathml" ) ) { try { i = h . root . toMathML ( "" ) . replace ( /\n */g , "" ) . replace ( /<!--.*?-->/g , "" ) } catch ( k ) { if ( ! k . restart ) { throw k } return MathJax . Callback . After ( [ "HandleMML" , this , l ] , k . restart ) } n . setAttribute ( "data-mathml" , i ) ; j = f . addElement ( n , "span" , { isMathJax : true , unselectable : "on" , className : "MJX_Assistive_MathML" + ( h . root . Get ( "display" ) === "block" ? " MJX_Assistive_MathML_Block" : "" ) } ) ; j . innerHTML = i ; n . style . position = "relative" ; n . setAttribute ( "role" , "presentation" ) ; n . firstChild . setAttribute ( "aria-hidden" , "true" ) ; j . setAttribute ( "role" , "presentation" ) } l . i ++ } l . callback ( ) } } ; b . Startup . signal . Post ( "AssistiveMML Ready" ) } ) ( MathJax . Ajax , MathJax . Callback , MathJax . Hub , MathJax . HTML ) ; MathJax . Callback . Queue ( [ "Require" , MathJax . Ajax , "[MathJax]/extensions/toMathML.js" ] , [ "loadComplete" , MathJax . Ajax , "[MathJax]/extensions/AssistiveMML.js" ] , function ( ) { MathJax . Hub . Register . StartupHook ( "End Config" , [ "Config" , MathJax . Extension . AssistiveMML ] ) } ) ;
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MathJax . Ajax . loadComplete ( "[MathJax]/config/MML_HTMLorMML-full.js" ) ;
