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/ *
* / M a t h J a x / c o n f i g / T e X - A M S _ H T M L - f u l l . j s
*
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* Copyright ( c ) 2010 - 2013 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 . Ajax . Preloading (
"[MathJax]/jax/input/TeX/config.js" ,
"[MathJax]/jax/output/HTML-CSS/config.js" ,
"[MathJax]/extensions/tex2jax.js" ,
"[MathJax]/extensions/MathEvents.js" ,
"[MathJax]/extensions/MathZoom.js" ,
"[MathJax]/extensions/MathMenu.js" ,
"[MathJax]/jax/element/mml/jax.js" ,
"[MathJax]/extensions/toMathML.js" ,
"[MathJax]/extensions/TeX/noErrors.js" ,
"[MathJax]/extensions/TeX/noUndefined.js" ,
"[MathJax]/jax/input/TeX/jax.js" ,
"[MathJax]/extensions/TeX/AMSmath.js" ,
"[MathJax]/extensions/TeX/AMSsymbols.js" ,
"[MathJax]/jax/output/HTML-CSS/jax.js" ,
"[MathJax]/jax/output/HTML-CSS/autoload/mtable.js"
) ;
MathJax . Hub . Config ( { "v1.0-compatible" : false } ) ;
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MathJax . InputJax . TeX = MathJax . InputJax ( { id : "TeX" , version : "2.2" , directory : MathJax . InputJax . directory + "/TeX" , extensionDir : MathJax . InputJax . extensionDir + "/TeX" , config : { TagSide : "right" , TagIndent : "0.8em" , MultLineWidth : "85%" , equationNumbers : { autoNumber : "none" , formatNumber : function ( a ) { return a } , formatTag : function ( a ) { return "(" + a + ")" } , formatID : function ( a ) { return "mjx-eqn-" + String ( a ) . replace ( /[:"'<>&]/g , "" ) } , formatURL : function ( a ) { return "#" + escape ( a ) } , useLabelIds : true } } } ) ; MathJax . InputJax . TeX . Register ( "math/tex" ) ; MathJax . InputJax . TeX . loadComplete ( "config.js" ) ;
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MathJax . OutputJax [ "HTML-CSS" ] = MathJax . OutputJax ( { id : "HTML-CSS" , version : "2.2" , 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" , 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_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" ) ;
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MathJax . Extension . tex2jax = { version : "2.2" , config : { inlineMath : [ [ "\\(" , "\\)" ] ] , displayMath : [ [ "$$" , "$$" ] , [ "\\[" , "\\]" ] ] , balanceBraces : true , skipTags : [ "script" , "noscript" , "style" , "textarea" , "pre" , "code" ] , ignoreClass : "tex2jax_ignore" , processClass : "tex2jax_process" , processEscapes : false , processEnvironments : true , processRefs : 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 } if ( this . createPatterns ( ) ) { this . scanElement ( a , a . nextSibling ) } } , createPatterns : function ( ) { var d = [ ] , e = [ ] , c , a , b = this . config ; this . match = { } ; for ( c = 0 , a = b . inlineMath . length ; 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 ] ) } } if ( d . length ) { e . push ( d . sort ( this . sortLength ) . join ( "|" ) ) } if ( b . processEnvironments ) { e . push ( "\\\\begin\\{([^}]*)\\}" ) } if ( b . processEscapes ) { e . push ( "\\\\*\\\\\\$" ) } if ( b . processRefs ) { e . push ( "\\\\(eq)?ref\\{[^}]*\\}" ) } this . start = new RegExp ( e . join ( "|" ) , "g" ) ; this . skipTags = new RegExp ( "^(" + b . skipTags . join ( "|" ) + ")$" , "i" ) ; var f = [ ] ; if ( MathJax . Hub . config . preRemoveClass ) { f . push ( MathJax . Hub . config . preRemoveClass ) } if ( b . ignoreClass ) { f . push ( b . ignoreClass ) } this . ignoreClass = ( f . length ? new RegExp ( "(^| )(" + f . join ( "|" ) + ")( |$)" ) : /^$/ ) ; this . processClass = new RegExp ( "(^| )(" + b . processClass + ")( |$)" ) ; return ( e . length > 0 ) } , 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 , g ) { var a , e , d , f ; while ( c && c != b ) { if ( c . nodeName . toLowerCase ( ) === "#text" ) { if ( ! g ) { 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 ) } f = this . processClass . exec ( a ) ; if ( c . firstChild && ! a . match ( /(^| )MathJax/ ) && ( f || ! this . skipTags . exec ( e ) ) ) { d = ( g || this . ignoreClass . exec ( a ) ) && ! f ; 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 ( this . search . close ? this . prevEndMatch ( ) : c ) } } } return b } , startMatch : function ( a , b ) { var f = this . match [ a [ 0 ] ] ; if ( f != null ) { this . search = { end : f . end , mode : f . mode , pcount : 0 , 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" , pcount : 0 , open : b , olen : 0 , opos : this . pattern . lastIndex - a [ 0 ] . length , isBeginEnd : true } ; this . switchPattern ( this . endPattern ( this . search . end ) ) } else { if ( a [ 0 ] . substr ( 0 , 4 ) === "\\ref" || a [ 0 ] . substr ( 0 , 6 ) === "\\eqref" ) { this . search = { mode : "" , end : "" , open : b , pcount : 0 , olen : 0 , opos : this . pattern . lastIndex - a [ 0 ] . length } ; return this . endMatch ( [ "" ] , b ) } 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 . insertBefor
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( function ( d , h , l , g , m , b , j ) { var q = "2.2" ; var i = MathJax . Extension ; var c = i . MathEvents = { version : q } ; var k = d . config . menuSettings ; var p = { hover : 500 , frame : { x : 3.5 , y : 5 , bwidth : 1 , bcolor : "#A6D" , hwidth : "15px" , hcolor : "#83A" } , button : { x : - 4 , y : - 3 , wx : - 2 , src : l . fileURL ( b . imageDir + "/MenuArrow-15.png" ) } , 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_Hover_Arrow" : { position : "absolute" , width : "15px" , height : "11px" , cursor : "pointer" } } } ; var n = c . Event = { LEFTBUTTON : 0 , RIGHTBUTTON : 2 , MENUKEY : "altKey" , Mousedown : function ( r ) { return n . Handler ( r , "Mousedown" , this ) } , Mouseup : function ( r ) { return n . Handler ( r , "Mouseup" , this ) } , Mousemove : function ( r ) { return n . Handler ( r , "Mousemove" , this ) } , Mouseover : function ( r ) { return n . Handler ( r , "Mouseover" , this ) } , Mouseout : function ( r ) { return n . Handler ( r , "Mouseout" , this ) } , Click : function ( r ) { return n . Handler ( r , "Click" , this ) } , DblClick : function ( r ) { return n . Handler ( r , "DblClick" , this ) } , Menu : function ( r ) { return n . Handler ( r , "ContextMenu" , this ) } , Handler : function ( u , s , t ) { if ( l . loadingMathMenu ) { return n . False ( u ) } var r = b [ t . jaxID ] ; if ( ! u ) { u = window . event } u . isContextMenu = ( s === "ContextMenu" ) ; if ( r [ s ] ) { return r [ s ] ( u , t ) } if ( i . MathZoom ) { return i . MathZoom . HandleEvent ( u , s , t ) } } , False : function ( r ) { if ( ! r ) { r = window . event } if ( r ) { if ( r . preventDefault ) { r . preventDefault ( ) } if ( r . stopPropagation ) { r . stopPropagation ( ) } r . cancelBubble = true ; r . returnValue = false } return false } , ContextMenu : function ( s , A , v ) { var x = b [ A . jaxID ] , u = x . getJaxFromMath ( A ) ; var B = ( x . config . showMathMenu != null ? x : d ) . config . showMathMenu ; if ( ! B || ( k . context !== "MathJax" && ! v ) ) { return } if ( c . msieEventBug ) { s = window . event || s } n . ClearSelection ( ) ; f . ClearHoverTimer ( ) ; if ( u . hover ) { if ( u . hover . remove ) { clearTimeout ( u . hover . remove ) ; delete u . hover . remove } u . hover . nofade = true } var t = MathJax . Menu ; var C , z ; if ( t ) { if ( t . loadingDomain ) { return n . False ( s ) } C = m . loadDomain ( "MathMenu" ) ; if ( ! C ) { t . jax = u ; var r = t . menu . Find ( "Show Math As" ) . menu ; r . items [ 0 ] . name = u . sourceMenuTitle ; r . items [ 0 ] . format = ( u . sourceMenuFormat || "MathML" ) ; r . items [ 1 ] . name = j [ u . inputJax ] . sourceMenuTitle ; var w = t . menu . Find ( "Math Settings" , "MathPlayer" ) ; w . hidden = ! ( u . outputJax === "NativeMML" && d . Browser . hasMathPlayer ) ; return t . menu . Post ( s ) } t . loadingDomain = true ; z = function ( ) { delete t . loadingDomain } } else { if ( l . loadingMathMenu ) { return n . False ( s ) } l . loadingMathMenu = true ; C = l . Require ( "[MathJax]/extensions/MathMenu.js" ) ; z = function ( ) { delete l . loadingMathMenu ; if ( ! MathJax . Menu ) { MathJax . Menu = { } } } } var y = { pageX : s . pageX , pageY : s . pageY , clientX : s . clientX , clientY : s . clientY } ; g . Queue ( C , z , [ "ContextMenu" , n , y , A , v ] ) ; return n . False ( s ) } , AltContextMenu : function ( t , s ) { var u = b [ s . jaxID ] ; var r = ( u . config . showMathMenu != null ? u : d ) . config . showMathMenu ; if ( r ) { r = ( u . config . showMathMenuMSIE != null ? u : d ) . config . showMathMenuMSIE ; if ( k . context === "MathJax" && ! k . mpContext && r ) { if ( ! c . noContextMenuBug || t . button !== n . RIGHTBUTTON ) { return } } else { if ( ! t [ n . MENUKEY ] || t . button !== n . LEFTBUTTON ) { return } } return u . ContextMenu ( t , s , true ) } } , ClearSelection : function ( ) { if ( c . safariContextMenuBug ) { setTimeout ( "window.getSelection().empty()" , 0 ) } if ( document . selection ) { setTimeout ( "document.selection.empty()" , 0 ) } } , getBBox : function ( t ) { t . appendChild ( c . topImg ) ; var s = c . topImg . offsetTop , u = t . offsetHeight - s , r = t . offsetWidth ; t . removeChild ( c . topImg ) ; return { w : r , h : s , d : u } } } ; var f = c . Hover = { Mouseover : function ( t , s ) { if ( k . discoverable || k . zoom === "Hover" ) { var v = t . fromElement || t . relatedTarget , u = t . toElement || t . target ; if ( v && u && ( v . isMathJax != u . isMathJax || d . getJaxFor ( v ) !== d . getJaxFor ( u ) ) ) { var r = this . getJaxFromMath ( s ) ; if ( r . hover ) { f . ReHover ( r ) } else { f . HoverTimer ( r , s ) } return n . False ( t ) } } } , Mouseout : function ( t , s ) { if ( k . discoverable || k . zoom === "Hover" ) { var v = t . fromElement || t . relatedTarget , u = t . toElement || t . target ; if ( v && u && ( v . isMathJax != u . isMathJax || d . getJaxFor ( v ) !== d . getJaxFor ( u ) ) ) { var r = this . getJaxFromMath ( s )
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( function ( a , d , f , c , j ) { var k = "2.2" ; 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" , "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" ) { return this . Zoom ( m , l ) } } , Hover : function ( m , l ) { if ( this . settings . zoom === "Hover" ) { this . Zoom ( m , l ) ; return true } return false } , Zoom : function ( n , s ) { this . Remove ( ) ; b . ClearHoverTimer ( ) ; g . ClearSelection ( ) ; var q = MathJax . OutputJax [ s . jaxID ] ; var o = q . getJaxFromMath ( s ) ; if ( o . hover ) { b . UnHover ( o ) } var l = Math . floor ( 0.85 * document . body . clientWidth ) , r = Math . floor ( 0.85 * Math . max ( document . body . clientHeight , document . documentElement . clientHeight ) ) ; var m = 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 , "max-width" : l + "px" , "max-height" : r + "px" } } , [ [ "span" , { style : { display : "inline-block" , "white-space" : "nowrap" } } ] ] ] ] ) ; var x = m . lastChild , u = x . firstChild , p = m . firstChild ; s . parentNode . insertBefore ( m , s ) ; s . parentNode . insertBefore ( s , m ) ; if ( u . addEventListener ) { u . addEventListener ( "mousedown" , this . Remove , true ) } if ( this . msieTrapEventBug ) { var w = d . Element ( "span" , { id : "MathJax_ZoomEventTrap" , onmousedown : this . Remove } ) ; m . insertBefore ( w , x ) } if ( this . msieZIndexBug ) { var t = d . addElement ( document . body , "img" , { src : "about:blank" , id : "MathJax_ZoomTracker" , width : 0 , height : 0 , style : { width : 0 , height : 0 , position : "relative" } } ) ; m . style . position = "relative" ; m . style . zIndex = i . styles [ "#MathJax_ZoomOverlay" ] [ "z-index" ] ; m = t } var v = q . Zoom ( o , u , s , l , r ) ; if ( this . msiePositionBug ) { if ( this . msieSizeBug ) { x . style . height = v . zH + "px" ; x . style . width = v . zW + "px" } if ( x . offsetHeight > r ) { x . style . height = r + "px" ; x . style . width = ( v . zW + this . scrollSize ) + "px" } if ( x . offsetWidth > l ) { x . style . width = l + "px" ; x . style . height = ( v . zH + this . scrollSize ) + "px" } } if ( this . operaPositionBug ) { x . style . width = Math . min ( l , v . zW ) + "px" } if ( x . offsetWidth && x . offsetWidth < l && x . offsetHeight < r ) { x . style . overflow = "visible" } this . Position ( x , v ) ; if ( this . msieTrapEventBug ) { w . style . height = x . clientHeight + "px" ; w . style . width = x . clientWidth + "px" ; w . style . left = ( parseFloat ( x . style . left ) + x . clientLeft ) + "px" ; w . style . top = ( parseFloat ( x . style . top ) + x . clientTop ) + "px" } x . style . visibility = "" ; if ( this . settings . zoom === "Hover" ) { p . onmouseover = this . Remove } if ( window . addEventListener ) { addEventListener ( "resize" , this . Resize , false ) } else { if ( window . attachEvent ) { attachEvent ( "onresize" , this . Resize ) } else { this . onresize = wind
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( function ( c , g , k , f , b ) { var q = "2.2" ; var j = MathJax . Callback . Signal ( "menu" ) ; MathJax . Extension . MathMenu = { version : q , signal : j } ; var o = function ( r ) { return MathJax . Localization . _ . apply ( MathJax . Localization , [ [ "MathMenu" , r ] ] . concat ( [ ] . slice . call ( arguments , 1 ) ) ) } ; var n = c . Browser . isPC , l = c . Browser . isMSIE , e = ( ( document . documentMode || 0 ) > 8 ) ; var i = ( n ? null : "5px" ) ; var p = c . CombineConfig ( "MathMenu" , { delay : 150 , closeImg : k . fileURL ( b . imageDir + "/CloseX-31.png" ) , showRenderer : true , showMathPlayer : true , showFontMenu : false , showContext : false , showDiscoverable : false , showLocale : true , showLocaleURL : false , 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_Menu" : { position : "absolute" , "background-color" : "white" , color : "black" , width : "auto" , padding : ( n ? "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 : ( n ? "2px 2em" : "1px 2em" ) , background : "transparent" } , ".MathJax_MenuArrow" : { position : "absolute" , right : ".5em" , color : "#666666" , "font-family" : ( l ? "'Arial unicode MS'" : null ) } , ".MathJax_MenuActive .MathJax_MenuArrow" : { color : "white" } , ".MathJax_MenuCheck" : { position : "absolute" , left : ".7em" , "font-family" : ( l ? "'Arial unicode MS'" : null ) } , ".MathJax_MenuRadioCheck" : { position : "absolute" , left : ( n ? "1em" : ".7em" ) } , ".MathJax_MenuLabel" : { padding : ( n ? "2px 2em 4px 1.33em" : "1px 2em 3px 1.33em" ) , "font-style" : "italic" } , ".MathJax_MenuRule" : { "border-top" : ( n ? "1px solid #CCCCCC" : "1px solid #DDDDDD" ) , margin : ( n ? "4px 1px 0px" : "4px 3px" ) } , ".MathJax_MenuDisabled" : { color : "GrayText" } , ".MathJax_MenuActive" : { "background-color" : ( n ? "Highlight" : "#606872" ) , color : ( n ? "HighlightText" : "white" ) } , ".MathJax_Menu_Close" : { position : "absolute" , width : "31px" , height : "31px" , top : "-15px" , left : "-15px" } } } ) ; var h , d ; c . Register . StartupHook ( "MathEvents Ready" , function ( ) { h = MathJax . Extension . MathEvents . Event . False ; d = MathJax . Extension . MathEvents . Hover } ) ; var a = MathJax . Menu = MathJax . Object . Subclass ( { version : q , items : [ ] , posted : false , title : null , margin : 5 , Init : function ( r ) { this . items = [ ] . slice . call ( arguments , 0 ) } , With : function ( r ) { if ( r ) { c . Insert ( this , r ) } return this } , Post : function ( s , B ) { if ( ! s ) { s = window . event } var r = document . getElementById ( "MathJax_MenuFrame" ) ; if ( ! r ) { r = a . Background ( this ) ; delete m . lastItem ; delete m . lastMenu ; delete a . skipUp ; j . Post ( [ "post" , a . jax ] ) } var t = g . addElement ( r , "div" , { onmouseup : a . Mouseup , ondblclick : h , ondragstart : h , onselectstart : h , oncontextmenu : h , menuItem : this , className : "MathJax_Menu" } ) ; MathJax . Localization . setCSS ( t ) ; for ( var v = 0 , u = this . items . length ; v < u ; v ++ ) { this . items [ v ] . Create ( t ) } if ( a . isMobile ) { g . addElement ( t , "span" , { className : "
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MathJax . ElementJax . mml = MathJax . ElementJax ( { mimeType : "jax/mml" } , { id : "mml" , version : "2.2" , 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" , 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 } , TEXCLASSNAMES : [ "ORD" , "OP" , "BIN" , "REL" , "OPEN" , "CLOSE" , "PUNCT" , "INNER" , "VCENTER" ] , copyAttributes : { fontfamily : true , fontsize : true , fontweight : true , fontstyle : true , color : true , background : true , id : true , "class" : true , href : true , style : true } , skipAttributes : { texClass : true , useHeight : true , texprimestyle : true } , copyAttributeNames : [ "fontfamily" , "fontsize" , "fontweight" , "fontstyle" , "color" , "background" , "id" , "class" , "href" , "style" ] } ) ; ( function ( a ) { a . mbase = MathJax . Object . Subclass ( { type : "base" , isToken : false , defaults : { mathbackground : a . INHERIT , mathcolor : a . INHERIT } , noInherit : { } , noInheritAttribute : { texClass : true } , linebreakContainer : false , Init : function ( ) { this . data = [ ] ; if ( this . inferRow && ! ( argum
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MathJax . Hub . Register . LoadHook ( "[MathJax]/jax/element/mml/jax.js" , function ( ) { var b = "2.2" ; var a = MathJax . ElementJax . mml ; SETTINGS = MathJax . Hub . config . menuSettings ; a . mbase . Augment ( { toMathML : function ( k ) { var g = ( this . inferred && this . parent . inferRow ) ; if ( k == null ) { k = "" } var e = this . type , d = this . toMathMLattributes ( ) ; 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 + ">" } , toMathMLattributes : function ( ) { var j = [ ] , g = this . defaults ; var c = ( this . attrNames || a . copyAttributeNames ) , l = a . skipAttributes ; if ( this . type === "math" && ( ! this . attr || ! this . attr . xmlns ) ) { j . push ( 'xmlns="http://www.w3.org/1998/Math/MathML"' ) } if ( ! this . attrNames ) { 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 . toMathMLattribute ( k ) + '"' ) } this [ d ] = k } } } } for ( var h = 0 , f = c . length ; h < f ; h ++ ) { if ( c [ h ] === "class" ) { continue } k = ( this . attr || { } ) [ c [ h ] ] ; if ( k == null ) { k = this [ c [ h ] ] } if ( k != null ) { j . push ( c [ h ] + '="' + this . toMathMLquote ( k ) + '"' ) } } this . toMathMLclass ( j ) ; if ( j . length ) { return " " + j . join ( " " ) } else { return "" } } , toMathMLclass : function ( c ) { var e = [ ] ; if ( this [ "class" ] ) { e . push ( this [ "class" ] ) } if ( this . isa ( a . TeXAtom ) && SETTINGS . texHints ) { var d = [ "ORD" , "OP" , "BIN" , "REL" , "OPEN" , "CLOSE" , "PUNCT" , "INNER" , "VCENTER" ] [ this . texClass ] ; if ( d ) { e . push ( "MJX-TeXAtom-" + d ) } } if ( this . mathvariant && this . toMathMLvariants [ this . mathvariant ] ) { e . push ( "MJX" + this . mathvariant ) } if ( this . arrow ) { e . push ( "MJX-arrow" ) } if ( this . variantForm ) { e . push ( "MJX-variant" ) } if ( e . length ) { c . unshift ( 'class="' + e . join ( " " ) + '"' ) } } , toMathMLattribute : function ( c ) { if ( typeof ( c ) === "string" && c . replace ( / /g , "" ) . match ( /^(([-+])?(\d+(\.\d*)?|\.\d+))mu$/ ) ) { return RegExp . $2 + ( ( 1 / 18 ) * RegExp . $3 ) . toFixed ( 3 ) . replace ( /\.?0+$/ , "" ) + "em" } else { if ( this . toMathMLvariants [ c ] ) { return this . toMathMLvariants [ c ] } } return this . toMathMLquote ( c ) } , 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 < 32 || k > 126 ) { 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 . 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 . toMathMLattributes ( ) ; 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 . toMathMLattributes ( ) ; 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 ( d ) { var c = this . toMathMLattributes ( ) ; if ( ! c && this . data [ 0 ] . data . length === 1 ) { return d . substr ( 2 ) + this . data [ 0 ] . toMathML ( d ) } return d + "<mrow" + c + ">\n" + this . data [ 0 ] . toMathML ( d + " " ) + "\n" + d + "</mrow>" } } ) ; a . chars . Augment ( { toMathML : function ( c ) { return ( c || "" ) + this . toMathMLquote ( this . toString ( ) ) } } ) ; a . entity . Augment ( { toMathML : function ( c ) { return ( c || "" ) + "&" + this . data [ 0 ] + ";<!-- " + this . toString ( ) + " -->" } } ) ; a . xml . Augment ( { toMathML : function ( c ) { return ( c || "" ) + this . to
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( function ( b , e ) { var d = "2.2" ; var a = b . CombineConfig ( "TeX.noErrors" , { disabled : false , multiLine : true , inlineDelimiters : [ "" , "" ] , style : { "font-size" : "90%" , "text-align" : "left" , color : "black" , padding : "1px 3px" , border : "1px solid" } } ) ; var c = "\u00A0" ; MathJax . Extension [ "TeX/noErrors" ] = { version : d , config : a } ; b . Register . StartupHook ( "TeX Jax Ready" , function ( ) { var f = MathJax . InputJax . TeX . formatError ; MathJax . InputJax . TeX . Augment ( { formatError : function ( j , i , k , g ) { if ( a . disabled ) { return f . apply ( this , arguments ) } var h = j . message . replace ( /\n.*/ , "" ) ; b . signal . Post ( [ "TeX Jax - parse error" , h , i , k , g ] ) ; var m = a . inlineDelimiters ; var l = ( k || a . multiLine ) ; if ( ! k ) { i = m [ 0 ] + i + m [ 1 ] } if ( l ) { i = i . replace ( / /g , c ) } else { i = i . replace ( /\n/g , " " ) } return MathJax . ElementJax . mml . merror ( i ) . With ( { isError : true , multiLine : l } ) } } ) } ) ; b . Register . StartupHook ( "HTML-CSS Jax Config" , function ( ) { b . Config ( { "HTML-CSS" : { styles : { ".MathJax .noError" : b . Insert ( { "vertical-align" : ( b . Browser . isMSIE && a . multiLine ? "-2px" : "" ) } , a . style ) } } } ) } ) ; b . Register . StartupHook ( "HTML-CSS Jax Ready" , function ( ) { var g = MathJax . ElementJax . mml ; var h = MathJax . OutputJax [ "HTML-CSS" ] ; var f = g . math . prototype . toHTML , i = g . merror . prototype . toHTML ; g . math . Augment ( { toHTML : function ( j , k ) { var l = this . data [ 0 ] ; if ( l && l . data [ 0 ] && l . data [ 0 ] . isError ) { j . style . fontSize = "" ; j = this . HTMLcreateSpan ( j ) ; j . bbox = l . data [ 0 ] . toHTML ( j ) . bbox } else { j = f . call ( this , j , k ) } return j } } ) ; g . merror . Augment ( { toHTML : function ( p ) { if ( ! this . isError ) { return i . call ( this , p ) } p = this . HTMLcreateSpan ( p ) ; p . className = "noError" ; if ( this . multiLine ) { p . style . display = "inline-block" } var r = this . data [ 0 ] . data [ 0 ] . data . join ( "" ) . split ( /\n/ ) ; for ( var o = 0 , l = r . length ; o < l ; o ++ ) { h . addText ( p , r [ o ] ) ; if ( o !== l - 1 ) { h . addElement ( p , "br" , { isMathJax : true } ) } } var q = h . getHD ( p . parentNode ) , k = h . getW ( p . parentNode ) ; if ( l > 1 ) { var n = ( q . h + q . d ) / 2 , j = h . TeX . x _height / 2 ; p . parentNode . style . verticalAlign = h . Em ( q . d + ( j - n ) ) ; q . h = j + n ; q . d = n - j } p . bbox = { h : q . h , d : q . d , w : k , lw : 0 , rw : k } ; return p } } ) } ) ; b . Register . StartupHook ( "SVG Jax Config" , function ( ) { b . Config ( { SVG : { styles : { ".MathJax_SVG .noError" : b . Insert ( { "vertical-align" : ( b . Browser . isMSIE && a . multiLine ? "-2px" : "" ) } , a . style ) } } } ) } ) ; b . Register . StartupHook ( "SVG Jax Ready" , function ( ) { var g = MathJax . ElementJax . mml ; var f = g . math . prototype . toSVG , h = g . merror . prototype . toSVG ; g . math . Augment ( { toSVG : function ( i , j ) { var k = this . data [ 0 ] ; if ( k && k . data [ 0 ] && k . data [ 0 ] . isError ) { i = k . data [ 0 ] . toSVG ( i ) } else { i = f . call ( this , i , j ) } return i } } ) ; g . merror . Augment ( { toSVG : function ( n ) { if ( ! this . isError || this . Parent ( ) . type !== "math" ) { return h . call ( this , n ) } n = e . addElement ( n , "span" , { className : "noError" , isMathJax : true } ) ; if ( this . multiLine ) { n . style . display = "inline-block" } var o = this . data [ 0 ] . data [ 0 ] . data . join ( "" ) . split ( /\n/ ) ; for ( var l = 0 , j = o . length ; l < j ; l ++ ) { e . addText ( n , o [ l ] ) ; if ( l !== j - 1 ) { e . addElement ( n , "br" , { isMathJax : true } ) } } if ( j > 1 ) { var k = n . offsetHeight / 2 ; n . style . verticalAlign = ( - k + ( k / j ) ) + "px" } return n } } ) } ) ; b . Register . StartupHook ( "NativeMML Jax Ready" , function ( ) { var h = MathJax . ElementJax . mml ; var g = MathJax . Extension [ "TeX/noErrors" ] . config ; var f = h . math . prototype . toNativeMML , i = h . merror . prototype . toNativeMML ; h . math . Augment ( { toNativeMML : function ( j ) { var k = this . data [ 0 ] ; if ( k && k . data [ 0 ] && k . data [ 0 ] . isError ) { j = k . data [ 0 ] . toNativeMML ( j ) } else { j = f . call ( this , j ) } return j } } ) ; h . merror . Augment ( { toNativeMML : function ( n ) { if ( ! this . isError ) { return i . call ( this , n ) } n = n . appendChild ( document . createElement ( "span" ) ) ; var o = this . data [ 0 ] . data [ 0 ] . data . join ( "" ) . split ( /\n/ ) ; for ( var l = 0 , k = o . length ; l < k ; l ++ ) { n . appendChild ( document . createTextNode ( o [ l ] ) ) ; if ( l !== k - 1 ) { n . appendChild ( document . createElement ( "br" ) ) } } if ( this . multiLine ) { n . style . display = "inline-block" ; if ( k > 1 ) { n . style . verticalAlign = "middle" } } for ( var p in g . style ) { if ( g . style . hasOwnProperty ( p ) ) { var j = p . replace ( /-./g , function ( m ) { return m . charAt ( 1 ) . toUpperCase ( ) } ) ; n . style [ j ] = g . style [ p ] } } return n } } ) } ) ; b . Startup . signal . Post ( "TeX noErrors Ready" ) } ) ( MathJax . Hub , MathJax . HTML ) ; MathJax . Ajax . loadComplete ( "[MathJax]/extensions/TeX/noErrors.js" ) ;
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MathJax . Extension [ "TeX/noUndefined" ] = { version : "2.2" , config : MathJax . Hub . CombineConfig ( "TeX.noUndefined" , { disabled : false , attributes : { mathcolor : "red" } } ) } ; MathJax . Hub . Register . StartupHook ( "TeX Jax Ready" , function ( ) { var b = MathJax . Extension [ "TeX/noUndefined" ] . config ; var a = MathJax . ElementJax . mml ; var c = MathJax . InputJax . TeX . Parse . prototype . csUndefined ; MathJax . InputJax . TeX . Parse . Augment ( { csUndefined : function ( d ) { if ( b . disabled ) { return c . apply ( this , arguments ) } MathJax . Hub . signal . Post ( [ "TeX Jax - undefined control sequence" , d ] ) ; this . Push ( a . mtext ( d ) . With ( b . attributes ) ) } } ) ; MathJax . Hub . Startup . signal . Post ( "TeX noUndefined Ready" ) } ) ; MathJax . Ajax . loadComplete ( "[MathJax]/extensions/TeX/noUndefined.js" ) ;
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( function ( d , c , i ) { var h , g = "\u00A0" ; var j = function ( l ) { return MathJax . Localization . _ . apply ( MathJax . Localization , [ [ "TeX" , l ] ] . concat ( [ ] . slice . call ( arguments , 1 ) ) ) } ; var e = MathJax . Object . Subclass ( { Init : function ( m , l ) { this . global = { isInner : l } ; this . data = [ b . start ( this . global ) ] ; if ( m ) { this . data [ 0 ] . env = m } this . env = this . data [ 0 ] . env } , Push : function ( ) { var n , l , o , p ; for ( n = 0 , l = arguments . length ; n < l ; n ++ ) { o = arguments [ n ] ; if ( o instanceof h . mbase ) { o = b . mml ( o ) } o . global = this . global ; p = ( this . data . length ? this . Top ( ) . checkItem ( o ) : true ) ; if ( p instanceof Array ) { this . Pop ( ) ; this . Push . apply ( this , p ) } else { if ( p instanceof b ) { this . Pop ( ) ; this . Push ( p ) } else { if ( p ) { this . data . push ( o ) ; if ( o . env ) { for ( var q in this . env ) { if ( this . env . hasOwnProperty ( q ) ) { o . env [ q ] = this . env [ q ] } } this . env = o . env } else { o . env = this . env } } } } } } , Pop : function ( ) { var l = this . data . pop ( ) ; if ( ! l . isOpen ) { delete l . env } this . env = ( this . data . length ? this . Top ( ) . env : { } ) ; return l } , Top : function ( l ) { if ( l == null ) { l = 1 } if ( this . data . length < l ) { return null } return this . data [ this . data . length - l ] } , Prev : function ( l ) { var m = this . Top ( ) ; if ( l ) { return m . data [ m . data . length - 1 ] } else { return m . Pop ( ) } } , toString : function ( ) { return "stack[\n " + this . data . join ( "\n " ) + "\n]" } } ) ; var b = e . Item = MathJax . Object . Subclass ( { type : "base" , endError : [ "ExtraOpenMissingClose" , "Extra open brace or missing close brace" ] , closeError : [ "ExtraCloseMissingOpen" , "Extra close brace or missing open brace" ] , rightError : [ "MissingLeftExtraRight" , "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 ( l , m ) { if ( l == null ) { l = true } if ( this . data . length === 1 && ! m ) { return this . data [ 0 ] } return h . mrow . apply ( h , this . data ) . With ( ( l ? { inferred : true } : { } ) ) } , checkItem : function ( l ) { if ( l . type === "over" && this . isOpen ) { l . num = this . mmlData ( false ) ; this . data = [ ] } if ( l . type === "cell" && this . isOpen ) { if ( l . linebreak ) { return false } d . Error ( [ "Misplaced" , "Misplaced %1" , l . name ] ) } if ( l . isClose && this [ l . type + "Error" ] ) { d . Error ( this [ l . type + "Error" ] ) } if ( ! l . isNotStack ) { return true } this . Push ( l . data [ 0 ] ) ; return false } , With : function ( l ) { for ( var m in l ) { if ( l . hasOwnProperty ( m ) ) { this [ m ] = l [ m ] } } return this } , toString : function ( ) { return this . type + "[" + this . data . join ( "; " ) + "]" } } ) ; b . start = b . Subclass ( { type : "start" , isOpen : true , Init : function ( l ) { this . SUPER ( arguments ) . Init . call ( this ) ; this . global = l } , checkItem : function ( l ) { if ( l . type === "stop" ) { return b . mml ( this . mmlData ( ) ) } return this . SUPER ( arguments ) . checkItem . call ( this , l ) } } ) ; b . stop = b . Subclass ( { type : "stop" , isClose : true } ) ; b . open = b . Subclass ( { type : "open" , isOpen : true , stopError : [ "ExtraOpenMissingClose" , "Extra open brace or missing close brace" ] , checkItem : function ( m ) { if ( m . type === "close" ) { var l = this . mmlData ( ) ; return b . mml ( h . TeXAtom ( l ) ) } return this . SUPER ( arguments ) . checkItem . call ( this , m ) } } ) ; b . close = b . Subclass ( { type : "close" , isClose : true } ) ; b . prime = b . Subclass ( { type : "prime" , checkItem : function ( l ) { if ( this . data [ 0 ] . type !== "msubsup" ) { return [ h . msup ( this . data [ 0 ] , this . data [ 1 ] ) , l ] } this . data [ 0 ] . SetData ( this . data [ 0 ] . sup , this . data [ 1 ] ) ; return [ this . data [ 0 ] , l ] } } ) ; b . subsup = b . Subclass ( { type : "subsup" , stopError : [ "MissingScript" , "Missing superscript or subscript argument" ] , supError : [ "MissingOpenForSup" , "Missing open brace for superscript" ] , subError : [ "MissingOpenForSup" , "Missing open brace for subscript" ] , checkItem : function ( l ) { if ( l . type === "open" || l . type === "left" ) { return true } if ( l . type === "mml" ) { if ( this . primes ) { if ( this . position !== 2 ) { this . data [ 0 ] . SetData ( 2 , this . primes ) } else { l . data [ 0 ] = h . mrow ( this . primes . With ( { variantForm : true } ) , l . data [ 0 ] ) } } 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 ( this [ [ "" , "subError" , "supError" ] [ this . position ] ] ) } } , Pop : function ( ) { } } ) ; b . over = b . Subclass ( { type : "over" , isClose : true , name : "\\over" , checkItem : function ( n , l ) { if ( n . type === "over" ) { d . Error ( [ "AmbiguousUseOf" , "Ambiguous use of %1" , n . name ] ) } if ( n . isClose ) { var m = h . mfrac ( this . num , this . mmlData ( false ) ) ; if ( this . thickness != null ) { m . linethickness = this . thickness } if ( this . open || this . close ) { m . texClass = h . TEXCLASS . INNER ; m . texWithDelims = true ; m
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MathJax . Extension [ "TeX/AMSmath" ] = { version : "2.2" , number : 0 , startNumber : 0 , labels : { } , eqlabels : { } , refs : [ ] } ; MathJax . Hub . Register . S tartupHook ( "TeX Jax Ready" , function ( ) { var b = MathJax . ElementJax . mml , g = MathJax . InputJax . TeX , f = MathJax . Extension [ "TeX/AMSmath" ] ; var d = g . Definitions , e = g . Stack . Item , a = g . config . equationNumbers ; var c = function ( j ) { var l = [ ] ; for ( var k = 0 , h = j . length ; k < h ; k ++ ) { l [ k ] = g . Parse . prototype . Em ( j [ k ] ) } return l . join ( " " ) } ; d . Add ( { mathchar0mo : { iiiint : [ "2A0C" , { texClass : b . TEXCLASS . OP } ] } , macros : { mathring : [ "Accent" , "2DA" ] , nobreakspace : "Tilde" , negmedspace : [ "Spacer" , b . LENGTH . NEGATIVEMEDIUMMATHSPACE ] , negthickspace : [ "Spacer" , b . LENGTH . NEGATIVETHICKMATHSPACE ] , idotsint : [ "MultiIntegral" , "\\int\\cdots\\int" ] , dddot : [ "Accent" , "20DB" ] , ddddot : [ "Accent" , "20DC" ] , sideset : [ "Macro" , "\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}" , 3 ] , boxed : [ "Macro" , "\\fbox{$\\displaystyle{#1}$}" , 1 ] , tag : "HandleTag" , notag : "HandleNoTag" , label : "HandleLabel" , ref : "HandleRef" , eqref : [ "HandleRef" , true ] , substack : [ "Macro" , "\\begin{subarray}{c}#1\\end{subarray}" , 1 ] , injlim : [ "NamedOp" , "inj lim" ] , projlim : [ "NamedOp" , "proj lim" ] , varliminf : [ "Macro" , "\\mathop{\\underline{\\mmlToken{mi}{lim}}}" ] , varlimsup : [ "Macro" , "\\mathop{\\overline{\\mmlToken{mi}{lim}}}" ] , varinjlim : [ "Macro" , "\\mathop{\\underrightarrow{\\mmlToken{mi}{lim}\\Rule{-1pt}{0pt}{1pt}}\\Rule{0pt}{0pt}{.45em}}" ] , varprojlim : [ "Macro" , "\\mathop{\\underleftarrow{\\mmlToken{mi}{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" , b . ALIGN . LEFT ] , shoveright : [ "HandleShove" , b . ALIGN . RIGHT ] , xrightarrow : [ "xArrow" , 8594 , 5 , 6 ] , xleftarrow : [ "xArrow" , 8592 , 7 , 3 ] } , environment : { align : [ "AMSarray" , null , true , true , "rlrlrlrlrlrl" , c ( [ 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 ] ) ] , "align*" : [ "AMSarray" , null , false , true , "rlrlrlrlrlrl" , c ( [ 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" , c ( [ 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 : [ "AlignedArray" , null , null , null , "rlrlrlrlrlrl" , c ( [ 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 , 2 , 5 / 18 ] ) , ".5em" , "D" ] , gathered : [ "AlignedArray" , null , null , null , "c" , null , ".5em" , "D" ] , subarray : [ "Array" , null , null , null , null , c ( [ 0 , 0 , 0 , 0 ] ) , "0.1em" , "S" , 1 ] , smallmatrix : [ "Array" , null , null , null , "c" , c ( [ 1 / 3 ] ) , ".2em" , "S" , 1 ] , equation : [ "EquationBegin" , "Equation" , true ] , "equation*" : [ "EquationBegin" , "EquationStar" , false ] , eqnarray : [ "AMSarray" , null , true , true , "rcl" , b . LENGTH . THICKMATHSPACE , ".5em" ] , "eqnarray*" : [ "AMSarray" , null , false , true , "rcl" , b . LENGTH . THICKMATHSPACE , ".5em" ] } , delimiter : { "\\lvert" : [ "2223" , { texClass : b . TEXCLASS . OPEN } ] , "\\rvert" : [ "2223" , { texClass : b . TEXCLASS . CLOSE } ] , "\\lVert" : [ "2225" , { texClass : b . TEXCLASS . OPEN } ] , "\\rVert" : [ "2225" , { texClass : b . TEXCLASS . CLOSE } ] } } , null , true ) ; g . Parse . Augment ( { HandleTag : function ( j ) { var l = this . GetStar ( ) ; var i = this . trimSpaces ( this . GetArgument ( j ) ) , h = i ; if ( ! l ) { i = a . formatTag ( i ) } var k = this . stack . global ; k . tagID = h ; if ( k . notags ) { g . Error ( [ "CommandNotAllowedInEnv" , "%1 not allowed in %2 environment" , j , k . notags ] ) } if ( k . tag ) { g . Error ( [ "MultipleCommand" , "Multiple %1" , j ] ) } k . tag = b . mtd . apply ( b , this . InternalMath ( i ) ) . With ( { id : a . formatID ( h ) } ) } , HandleNoTag : function ( h ) { if ( this . stack . global . tag ) { delete this . stack . global . tag } this . stack . global . notag = true } , HandleLabel : function ( i ) { var j = this . stack . global , h = this . GetArgument ( i ) ; if ( h === "" ) { return } if ( ! f . refUpdate ) { if ( j . label ) { g . Error ( [ "MultipleCommand" , "Multiple %1" , i ] ) } j . label = h ; if ( f . labels [ h ] || f . eqlabels [ h ] ) { g . Error ( [ "MultipleLabel" , "Label '%1' multiply defined" , h ] ) } f . eqlabels [ h ] = "???" } } , HandleRef : function ( j , l ) { var i = this . GetArgument ( j ) ; var k = f . labels [ i ] || f . eqlabels [ i ] ; if ( ! k ) { k = "??" ; f . badref = ! f .
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MathJax . Extension [ "TeX/AMSsymbols" ] = { version : "2.2" } ; MathJax . Hub . Register . StartupHook ( "TeX Jax Ready" , function ( ) { var a = MathJax . ElementJax . mml , b = MathJax . InputJax . TeX . Definitions ; b . Add ( { mathchar0mi : { digamma : "03DD" , varkappa : "03F0" , varGamma : [ "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" , varnothing : [ "2205" , { variantForm : true } ] , blacktriangle : "25B4" , triangledown : [ "25BD" , { variantForm : true } ] , blacktriangledown : "25BE" , square : "25FB" , Box : "25FB" , blacksquare : "25FC" , 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" , 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" , { variantForm : true } ] , subseteqq : "2AC5" , supseteqq : "2AC6" , Subset : "22D0" , Supset : "22D1" , sqsubset : "228F" , sqsupset : "2290" , preccurlyeq : "227C" , succcurlyeq : "227D" , curlyeqprec : "22DE" , curlyeqsucc : "22DF" , precsim : "227E" , succsim : "227F" , precapprox : "2AB7" , succapprox : "2AB8" , vartriangleleft : "22B2" , lhd : "22B2" , vartriangleright : "22B3" , rhd : "22B3" , trianglelefteq : "22B4" , unlhd : "22B4" , trianglerighteq : "22B5" , unrhd : "22B5" , vDash : "22A8" , Vdash : "22A9" , Vvdash : "22AA" , smallsmile : [ "2323" , { variantForm : true } ] , shortmid : [ "2223" , { variantForm : true } ] , smallfrown : [ "2322" , { variantForm : true } ] , shortparallel : [ "2225" , { variantForm : true } ] , bumpeq : "224F" , between : "226C" , Bumpeq : "224E" , pitchfork : "22D4" , varpropto : "221D" , backepsilon : "220D" , blacktriangleleft : "25C2" , blacktriangleright : "25B8" , therefore : "2234" , because : "2235" , eqsim : "2242" , vartriangle : [ "25B3" , { variantForm : true } ] , Join : "22C8" , nless : "226E" , ngtr : "226F" , nleq : "2270" , ngeq : "2271" , nleqslant : [ "2A87" , { variantForm : true } ] , ngeqslant : [ "2A88" , { variantForm : true } ] , nleqq : [ "2270" , { variantForm : true } ] , ngeqq : [ "2271" , { variantForm : true } ] , lneq : "2A87" , gneq : "2A88" , lneqq : "2268" , gneqq : "2269" , lvertneqq : [ "2268" , { variantForm : true } ] , gvertneqq : [ "2269" , { variantForm : true } ] , lnsim : "22E6" , gnsim : "22E7" , lnapprox : "2A89" , gnapprox : "2A8A" , nprec : "2280" , nsucc : "2281" , npreceq : [ "22E0" , { variantForm : true } ] , nsucceq : [ "22E1" , { variantForm : true } ] , precneqq : "2AB5" , succneqq : "2AB6" , precnsim : "22E8" , succnsim : "22E9" , precnapprox : "2AB9" , succnapprox : "2ABA" , nsim : "2241" , ncong : "2246" , nshortmid : [ "2224" , { variantForm : true } ] , nshortparallel : [ "2226" , { variantForm : true } ] , nmid : "2224" , nparallel : "2226" , nvdash : "22AC" , nvDash : "22AD" , nVdash : "22AE" , nVDash : "22AF" , ntriangleleft : "22EA" , ntriangleright : "22EB" , ntrianglelefteq : "22EC" , ntri
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( 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 , FontInfo : { STIX : { family : "STIXSizeOneSym" , testString : "() {} []" } , TeX : { family : "MathJax_Size1" , testString : "() {} []" } } , comparisonFont : [ "sans-serif" , "monospace" , "script" , "Times" , "Courier" , "Arial" , "Helvetica" ] , testSize : [ "40px" , "50px" , "60px" , "30px" , "20px" ] , Init : function ( ) { this . div = MathJax . HTML . addElement ( document . body , "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" } } , [ "" ] ) ; this . text = this . div . firstChild } , findFont : function ( o , l ) { if ( l && this . testCollection ( l ) ) { return l } for ( var n = 0 , k = o . length ; n < k ; n ++ ) { if ( o [ n ] === l ) { continue } if ( this . testCollection ( o [ n ] ) ) { return o [ n ] } } return null } , testCollection : function ( k ) { return this . testFont ( this . FontInfo [ 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 l = this . getComparisonWidths ( n . testString , n . noStyleChar ) ; if ( l ) { this . div . style . fontFamily = "'" + n . family + "'," + this . comparisonFont [ 0 ] ; if ( this . div . offsetWidth == l [ 0 ] ) { this . div . style . fontFamily = "'" + n . family + "'," + this . comparisonFont [ l [ 2 ] ] ; if ( this . div . offsetWidth == l [ 1 ] ) { return false } } if ( this . div . offsetWidth != l [ 3 ] || this . div . offsetHeight != l [ 4 ] ) { if ( n . noStyleChar || ! d . FONTDATA || ! d . FONTDATA . hasStyleChar ) { return true } for ( var o = 0 , k = this . testSize . length ; o < k ; o ++ ) { if ( this . testStyleChar ( n , this . testSize [ o ] ) ) { return true } } } } return false } , 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 . Callback ( [ "loadComplete" , this , l , o , k ] ) ; h . timer . start ( h , [ this . checkWebFont , l , m ] , 0 , this . timeout ) ; return k } , loadComplete : function ( m , p , l , k ) { MathJax . Message . Clear ( p ) ; if ( k === h . STATUS . OK ) { this . webFontLoaded = true ; l ( ) ; return } this . loadError ( m ) ; if ( b . Browser . isFirefox && d . allowWebFonts ) { var o = document . location . protocol + "//" + document . location . hostname ; if ( document . location . port != "" ) { o += ":" + document . location . port } o += "/" ; if ( h . fileURL ( d . webfontDir ) . substr ( 0 , o . length ) !== o ) { this . firefoxFontError ( m ) } } if ( ! this . webFontLoaded ) { d . loadWebFontError ( m , l ) } else { l ( ) } } , loadError : function ( k ) { e ( [ "CantLoadWebFont" , "Can't load web font %1" , d . fontInUse + "/" + k . directory ] , null , 2000 )
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MathJax . Hub . Register . StartupHook ( "HTML-CSS Jax Ready" , function ( ) { var c = "2.2" ; var a = MathJax . ElementJax . mml , b = MathJax . OutputJax [ "HTML-CSS" ] ; a . mtable . Augment ( { toHTML : function ( t ) { t = this . HTMLcreateSpan ( t ) ; if ( this . data . length === 0 ) { return t } var K = this . getValues ( "columnalign" , "rowalign" , "columnspacing" , "rowspacing" , "columnwidth" , "equalcolumns" , "equalrows" , "columnlines" , "rowlines" , "frame" , "framespacing" , "align" , "useHeight" , "width" , "side" , "minlabelspacing" ) ; var aJ = K . width . match ( /%$/ ) ; var ay = b . createStack ( t ) ; var aG = this . HTMLgetScale ( ) , aA = this . HTMLgetMu ( t ) , aB = - 1 ; var aq = [ ] , au = [ ] , ak = [ ] , aw = [ ] , av = [ ] , af , ae , ap = - 1 , ad , ao , Z , aF , R , aC , aO = [ ] ; var al = b . FONTDATA . baselineskip * aG * K . useHeight , aT , I = b . FONTDATA . lineH * aG , O = b . FONTDATA . lineD * aG ; for ( af = 0 , ad = this . data . length ; af < ad ; af ++ ) { aF = this . data [ af ] ; Z = ( aF . type === "mlabeledtr" ? aB : 0 ) ; aw [ af ] = [ ] ; aq [ af ] = au [ af ] = 0 ; for ( ae = Z , ao = aF . data . length + Z ; ae < ao ; ae ++ ) { if ( ak [ ae ] == null ) { if ( ae > ap ) { ap = ae } av [ ae ] = b . createStack ( b . createBox ( ay ) ) ; ak [ ae ] = - b . BIGDIMEN } aw [ af ] [ ae ] = b . createBox ( av [ ae ] ) ; aO . push ( aF . data [ ae - Z ] . toHTML ( aw [ af ] [ ae ] ) ) } } b . MeasureSpans ( aO ) ; for ( af = 0 , ad = this . data . length ; af < ad ; af ++ ) { aF = this . data [ af ] ; Z = ( aF . type === "mlabeledtr" ? aB : 0 ) ; for ( ae = Z , ao = aF . data . length + Z ; ae < ao ; ae ++ ) { R = aF . data [ ae - Z ] ; if ( R . isMultiline ) { aw [ af ] [ ae ] . style . width = "100%" } if ( R . isEmbellished ( ) ) { aC = R . CoreMO ( ) ; var aS = aC . Get ( "minsize" , true ) ; if ( aS ) { var aL = aC . HTMLspanElement ( ) . bbox ; if ( aC . HTMLcanStretch ( "Vertical" ) ) { aT = aL . h + aL . d ; if ( aT ) { aS = b . length2em ( aS , aA , aT ) ; if ( aS * aL . h / aT > aq [ ae ] ) { aq [ ae ] = aS * aL . h / aT } if ( aS * aL . d / aT > au [ ae ] ) { au [ ae ] = aS * aL . d / aT } } } else { if ( aC . HTMLcanStretch ( "Horizontal" ) ) { aS = b . length2em ( aS , aA , aL . w ) ; if ( aS > ak [ ae ] ) { ak [ ae ] = aS } } } } } if ( aw [ af ] [ ae ] . bbox . h > aq [ af ] ) { aq [ af ] = aw [ af ] [ ae ] . bbox . h } if ( aw [ af ] [ ae ] . bbox . d > au [ af ] ) { au [ af ] = aw [ af ] [ ae ] . bbox . d } if ( aw [ af ] [ ae ] . bbox . w > ak [ ae ] ) { ak [ ae ] = aw [ af ] [ ae ] . bbox . w } } } if ( aq [ 0 ] + au [ 0 ] ) { aq [ 0 ] = Math . max ( aq [ 0 ] , I ) } if ( aq [ aw . length - 1 ] + au [ aw . length - 1 ] ) { au [ aw . length - 1 ] = Math . max ( au [ aw . length - 1 ] , O ) } var aE = MathJax . Hub . SplitList ; var az = aE ( K . columnspacing ) , aQ = aE ( K . rowspacing ) , e = aE ( K . columnalign ) , E = aE ( K . rowalign ) , d = aE ( K . columnlines ) , z = aE ( K . rowlines ) , aM = aE ( K . columnwidth ) , V = [ ] ; for ( af = 0 , ad = az . length ; af < ad ; af ++ ) { az [ af ] = b . length2em ( az [ af ] , aA ) } for ( af = 0 , ad = aQ . length ; af < ad ; af ++ ) { aQ [ af ] = b . length2em ( aQ [ af ] , aA ) } while ( az . length < ap ) { az . push ( az [ az . length - 1 ] ) } while ( e . length <= ap ) { e . push ( e [ e . length - 1 ] ) } while ( d . length < ap ) { d . push ( d [ d . length - 1 ] ) } while ( aM . length <= ap ) { aM . push ( aM [ aM . length - 1 ] ) } while ( aQ . length < aw . length ) { aQ . push ( aQ [ aQ . length - 1 ] ) } while ( E . length <= aw . length ) { E . push ( E [ E . length - 1 ] ) } while ( z . length < aw . length ) { z . push ( z [ z . length - 1 ] ) } if ( av [ aB ] ) { e [ aB ] = ( K . side . substr ( 0 , 1 ) === "l" ? "left" : "right" ) ; az [ aB ] = - ak [ aB ] } for ( af = 0 , ad = aw . length ; af < ad ; af ++ ) { aF = this . data [ af ] ; V [ af ] = [ ] ; if ( aF . rowalign ) { E [ af ] = aF . rowalign } if ( aF . columnalign ) { V [ af ] = aE ( aF . columnalign ) ; while ( V [ af ] . length <= ap ) { V [ af ] . push ( V [ af ] [ V [ af ] . length - 1 ] ) } } } if ( K . equalrows ) { var aD = Math . max . apply ( Math , aq ) , X = Math . max . apply ( Math , au ) ; for ( af = 0 , ad = aw . length ; af < ad ; af ++ ) { Z = ( ( aD + X ) - ( aq [ af ] + au [ af ] ) ) / 2 ; aq [ af ] += Z ; au [ af ] += Z } } aT = aq [ 0 ] + au [ aw . length - 1 ] ; for ( af = 0 , ad = aw . length - 1 ; af < ad ; af ++ ) { aT += Math . max ( ( aq [ af ] + au [ af ] ? al : 0 ) , au [ af ] + aq [ af + 1 ] + aQ [ af ] ) } var aI = 0 , aH = 0 , aV , g = aT ; if ( K . frame !== "none" || ( K . columnlines + K . rowlines ) . match ( /solid|dashed/ ) ) { var w = aE ( K . framespacing ) ; if ( w . length != 2 ) { w = aE ( this . defaults . framespacing ) } aI = b . length2em ( w [ 0 ] , aA ) ; aH = b . length2em ( w [ 1 ] , aA ) ; g = aT + 2 * aH } var aj , aU , ab = "" ; if ( typeof ( K . align ) !== "string" ) { K . align = String ( K . align ) } if ( K . align . match ( /(top|bottom|center|baseline|axis)( +(-?\d+))?/ ) ) { ab = RegExp . $3 ; K . align = RegExp . $1 } else { K . align = this . defaults . align } if ( ab !== "" ) { ab = parseInt ( ab ) ; if ( ab < 0 ) { ab = aw . length + 1 + ab } if ( ab < 1 ) { ab = 1 } else { if ( ab > aw . length ) { ab = aw . length } } aj = 0 ; aU = - ( aT + aH ) + aq [ 0 ] ; for ( af = 0 , ad = ab - 1 ; af < ad ; af ++ ) { var N = Math . max ( ( aq [ af ] + au [ af ] ? al : 0 ) , au [ af ] + aq [ af + 1 ] + aQ [ af ] ) ; aj += N ; aU += N } } else { aj = ( { top : - ( aq [ 0 ] + aH ) , bottom : aT + aH - aq [ 0 ] , center : aT / 2 - aq [ 0 ] , baseline : aT / 2 - aq [ 0 ] , axis : aT / 2 + b . TeX . axis _height * aG - aq [ 0 ] } ) [ K . align ] ; aU = ( { top : - ( aT + 2 * aH ) , bottom : 0 , center : - ( aT / 2 + aH ) , baseline : - ( aT / 2 + aH ) , axis : b . TeX . axis _height * aG - aT / 2 - aH } ) [ K . align ] } var ac , ag = 0 , B = 0 , L = 0 , aa = 0 , ah = 0 , an = [ ] , at = [ ] , S = 1 ; if ( K . equalcolumns && K . width !== "auto" ) { if ( aJ ) { ac = ( 100 / ( ap + 1 ) ) . toFixed ( 2 ) . rep
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MathJax . Ajax . loadComplete ( "[MathJax]/config/TeX-AMS_HTML-full.js" ) ;
