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TeX-AMS-MML_SVG-full.js

TeX-AMS-MML_SVG-full.js 233 KB
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  1. /*
    2. 

  2.  *  /MathJax/config/TeX-AMS-MML_SVG-full.js
    3. 

  3.  *  
    4. 

  4.  *  Copyright (c) 2010-2013 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Part of the MathJax library.
    7. 

  7.  *  See http://www.mathjax.org for details.
    8. 

  8.  * 
    9. 

  9.  *  Licensed under the Apache License, Version 2.0;
    10. 

  10.  *  you may not use this file except in compliance with the License.
    11. 

  11.  *
    12. 

  12.  *      http://www.apache.org/licenses/LICENSE-2.0
    13. 

  13.  */
    14. 

  14. 

  15. MathJax.Ajax.Preloading(
    16. 

  16.   "[MathJax]/jax/input/TeX/config.js",
    17. 

  17.   "[MathJax]/jax/input/MathML/config.js",
    18. 

  18.   "[MathJax]/jax/output/SVG/config.js",
    19. 

  19.   "[MathJax]/extensions/tex2jax.js",
    20. 

  20.   "[MathJax]/extensions/mml2jax.js",
    21. 

  21.   "[MathJax]/extensions/MathEvents.js",
    22. 

  22.   "[MathJax]/extensions/MathZoom.js",
    23. 

  23.   "[MathJax]/extensions/MathMenu.js",
    24. 

  24.   "[MathJax]/jax/element/mml/jax.js",
    25. 

  25.   "[MathJax]/extensions/toMathML.js",
    26. 

  26.   "[MathJax]/extensions/TeX/noErrors.js",
    27. 

  27.   "[MathJax]/extensions/TeX/noUndefined.js",
    28. 

  28.   "[MathJax]/jax/input/TeX/jax.js",
    29. 

  29.   "[MathJax]/extensions/TeX/AMSmath.js",
    30. 

  30.   "[MathJax]/extensions/TeX/AMSsymbols.js",
    31. 

  31.   "[MathJax]/jax/input/MathML/jax.js",
    32. 

  32.   "[MathJax]/jax/output/SVG/jax.js",
    33. 

  33.   "[MathJax]/jax/output/SVG/autoload/mtable.js"
    34. 

  34. );
    35. 

  35. 

  36. MathJax.Hub.Config({"v1.0-compatible":false});
    37. 

  37. 

  38. MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.2.1",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");
    39. 

  39. 

  40. MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.2",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");
    41. 

  41. 

  42. MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.2",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:10,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js");
    43. 

  43. 

  44. 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.insertBefore(e,c);this.pattern.lastIndex=g}}}return b},endMatch:function(a,c){var b=this.search;if(a[0]==b.end){if(!b.close||b.pcount===0){b.close=c;b.cpos=this.pattern.lastIndex;b.clen=(b.isBeginEnd?0:a[0].length)}if(b.pcount===0){b.matched=true;c=this.encloseMath(c);this.switchPattern(this.start)}}else{if(a[0]==="{"){b.pcount++}else{if(a[0]==="}"&&b.pcount){b.pcount--}}}return c},prevEndMatch:function(){this.search.matched=true;var a=this.encloseMath(this.search.close);this.switchPattern(this.start);return a},switchPattern:function(a){a.lastIndex=this.pattern.lastIndex;this.pattern=a;this.search.start=(a===this.start)},encloseMath:function(b){var a=this.search,f=a.close,e,c;if(a.cpos===f.length){f=f.nextSibling}else{f=f.splitText(a.cpos)}if(!f){e=f=MathJax.HTML.addText(a.close.parentNode,"")}a.close=f;c=(a.opos?a.open.splitText(a.opos):a.open);while(c.nextSibling&&c.nextSibling!==f){if(c.nextSibling.nodeValue!==null){if(c.nextSibling.nodeName==="#comment"){c.nodeValue+=c.nextSibling.nodeValue.replace(/^\[CDATA\[((.|\n|\r)*)\]\]$/,"$1")}else{c.nodeValue+=c.nextSibling.nodeValue}}else{if(this.msieNewlineBug){c.nodeValue+=(c.nextSibling.nodeName.toLowerCase()==="br"?"\n":" ")}else{c.nodeValue+=" "}}c.parentNode.removeChild(c.nextSibling)}var d=c.nodeValue.substr(a.olen,c.nodeValue.length-a.olen-a.clen);c.parentNode.removeChild(c);if(this.config.preview!=="none"){this.createPreview(a.mode,d)}c=this.createMathTag(a.mode,d);this.search={};this.pattern.lastIndex=0;if(e){e.parentNode.removeChild(e)}return c},insertNode:function(b){var a=this.search;a.close.parentNode.insertBefore(b,a.close)},createPreview:function(c,a){var b=this.config.preview;if(b==="none"){return}if(b==="TeX"){b=[this.filterPreview(a)]}if(b){b=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},b);this.insertNode(b)}},createMathTag:function(c,b){var a=document.createElement("script");a.type="math/tex"+c;MathJax.HTML.setScript(a,b);this.insertNode(a);return a},filterPreview:function(a){return a},msieNewlineBug:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9)};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.tex2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/tex2jax.js");
    45. 

  45. 

  46. MathJax.Extension.mml2jax={version:"2.2",config:{preview:"alttext"},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}this.ProcessMathArray(e.getElementsByTagName("math"));if(e.getElementsByTagNameNS){this.ProcessMathArray(e.getElementsByTagNameNS(this.MMLnamespace,"math"))}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.ProcessMathArray(e.getElementsByTagName(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.ProcessMathArray(e.getElementsByTagName(a.nodeName.substr(6)+":math"))}}}}},ProcessMathArray:function(b){var a;if(b.length){if(this.MathTagBug){for(a=b.length-1;a>=0;a--){if(b[a].nodeName==="MATH"){this.ProcessMathFlattened(b[a])}else{this.ProcessMath(b[a])}}}else{for(a=b.length-1;a>=0;a--){this.ProcessMath(b[a])}}}},ProcessMath:function(e){var d=e.parentNode;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(/&nbsp;/g,"&#xA0;")}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;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){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,"&#x26;").replace(/</g,"&lt;").replace(/>/g,"&gt;").replace(/\"/g,"&quot;")},createPreview:function(b,a){var c=this.config.preview;if(c==="none"){return}if(c==="alttext"){var d=b.getAttribute("alttext");if(d!=null){c=[this.filterPreview(d)]}else{c=null}}if(c){c=MathJax.HTML.Element("span",{className:MathJax.Hub.config.preRemoveClass},c);a.parentNode.insertBefore(c,a)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"<math><mi>x</mi><mspace /></math>"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="&lt;"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax]);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js");
    47. 

  47. 

  48. (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);if(r.hover){f.UnHover(r)}else{f.ClearHoverTimer()}return n.False(t)}}},Mousemove:function(t,s){if(k.discoverable||k.zoom==="Hover"){var r=this.getJaxFromMath(s);if(r.hover){return}if(f.lastX==t.clientX&&f.lastY==t.clientY){return}f.lastX=t.clientX;f.lastY=t.clientY;f.HoverTimer(r,s);return n.False(t)}},HoverTimer:function(r,s){this.ClearHoverTimer();this.hoverTimer=setTimeout(g(["Hover",this,r,s]),p.hover)},ClearHoverTimer:function(){if(this.hoverTimer){clearTimeout(this.hoverTimer);delete this.hoverTimer}},Hover:function(r,v){if(i.MathZoom&&i.MathZoom.Hover({},v)){return}var u=b[r.outputJax],w=u.getHoverSpan(r,v),z=u.getHoverBBox(r,w,v),x=(u.config.showMathMenu!=null?u:d).config.showMathMenu;var B=p.frame.x,A=p.frame.y,y=p.frame.bwidth;if(c.msieBorderWidthBug){y=0}r.hover={opacity:0,id:r.inputID+"-Hover"};var s=h.Element("span",{id:r.hover.id,isMathJax:true,style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Frame",isMathJax:true,style:{display:"inline-block",position:"absolute",top:this.Px(-z.h-A-y-(z.y||0)),left:this.Px(-B-y+(z.x||0)),width:this.Px(z.w+2*B),height:this.Px(z.h+z.d+2*A),opacity:0,filter:"alpha(opacity=0)"}}]]);var t=h.Element("span",{isMathJax:true,id:r.hover.id+"Menu",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["img",{className:"MathJax_Hover_Arrow",isMathJax:true,math:v,src:p.button.src,onclick:this.HoverMenu,jax:u.id,style:{left:this.Px(z.w+B+y+(z.x||0)+p.button.x),top:this.Px(-z.h-A-y-(z.y||0)-p.button.y),opacity:0,filter:"alpha(opacity=0)"}}]]);if(z.width){s.style.width=t.style.width=z.width;s.style.marginRight=t.style.marginRight="-"+z.width;s.firstChild.style.width=z.width;t.firstChild.style.left="";t.firstChild.style.right=this.Px(p.button.wx)}w.parentNode.insertBefore(s,w);if(x){w.parentNode.insertBefore(t,w)}if(w.style){w.style.position="relative"}this.ReHover(r)},ReHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}r.hover.remove=setTimeout(g(["UnHover",this,r]),p.fadeoutDelay);this.HoverFadeTimer(r,p.fadeinInc)},UnHover:function(r){if(!r.hover.nofade){this.HoverFadeTimer(r,-p.fadeoutInc,p.fadeoutStart)}},HoverFade:function(r){delete r.hover.timer;r.hover.opacity=Math.max(0,Math.min(1,r.hover.opacity+r.hover.inc));r.hover.opacity=Math.floor(1000*r.hover.opacity)/1000;var t=document.getElementById(r.hover.id),s=document.getElementById(r.hover.id+"Menu");t.firstChild.style.opacity=r.hover.opacity;t.firstChild.style.filter="alpha(opacity="+Math.floor(100*r.hover.opacity)+")";if(s){s.firstChild.style.opacity=r.hover.opacity;s.firstChild.style.filter=t.style.filter}if(r.hover.opacity===1){return}if(r.hover.opacity>0){this.HoverFadeTimer(r,r.hover.inc);return}t.parentNode.removeChild(t);if(s){s.parentNode.removeChild(s)}if(r.hover.remove){clearTimeout(r.hover.remove)}delete r.hover},HoverFadeTimer:function(r,t,s){r.hover.inc=t;if(!r.hover.timer){r.hover.timer=setTimeout(g(["HoverFade",this,r]),(s||p.fadeDelay))}},HoverMenu:function(r){if(!r){r=window.event}return b[this.jax].ContextMenu(r,this.math,true)},ClearHover:function(r){if(r.hover.remove){clearTimeout(r.hover.remove)}if(r.hover.timer){clearTimeout(r.hover.timer)}f.ClearHoverTimer();delete r.hover},Px:function(r){if(Math.abs(r)<0.006){return"0px"}return r.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){var r=new Image();r.src=p.button.src}};var a=c.Touch={last:0,delay:500,start:function(s){var r=new Date().getTime();var t=(r-a.last<a.delay&&a.up);a.last=r;a.up=false;if(t){a.timeout=setTimeout(a.menu,a.delay,s,this);s.preventDefault()}},end:function(s){var r=new Date().getTime();a.up=(r-a.last<a.delay);if(a.timeout){clearTimeout(a.timeout);delete a.timeout;a.last=0;a.up=false;s.preventDefault();return n.Handler((s.touches[0]||s.touch),"DblClick",this)}},menu:function(s,r){delete a.timeout;a.last=0;a.up=false;return n.Handler((s.touches[0]||s.touch),"ContextMenu",r)}};if(d.Browser.isMobile){var o=p.styles[".MathJax_Hover_Arrow"];o.width="25px";o.height="18px";p.button.x=-6}d.Browser.Select({MSIE:function(r){var t=(document.documentMode||0);var s=r.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=r.isIE9;c.msieAlignBug=(!s||t<8);if(t<9){n.LEFTBUTTON=1}},Safari:function(r){c.safariContextMenuBug=true},Opera:function(r){c.operaPositionBug=true},Konqueror:function(r){c.noContextMenuBug=true}});c.topImg=(c.msieAlignBug?h.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):h.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(c.operaPositionBug){c.topImg.style.border="1px solid"}c.config=p=d.CombineConfig("MathEvents",p);var e=function(){var r=p.styles[".MathJax_Hover_Frame"];r.border=p.frame.bwidth+"px solid "+p.frame.bcolor+" ! important";r["box-shadow"]=r["-webkit-box-shadow"]=r["-moz-box-shadow"]=r["-khtml-box-shadow"]="0px 0px "+p.frame.hwidth+" "+p.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,p.styles],["Post",d.Startup.signal,"MathEvents Ready"],["loadComplete",l,"[MathJax]/extensions/MathEvents.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.Callback,MathJax.Localization,MathJax.OutputJax,MathJax.InputJax);
    49. 

  49. 

  50. (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=window.onresize;window.onresize=this.Resize}}a.signal.Post(["math zoomed",o]);return e(n)},Position:function(p,r){var q=this.Resize(),m=q.x,s=q.y,l=r.mW;var o=-l-Math.floor((p.offsetWidth-l)/2),n=r.Y;p.style.left=Math.max(o,10-m)+"px";p.style.top=Math.max(n,10-s)+"px";if(!h.msiePositionBug){h.SetWH()}},Resize:function(m){if(h.onresize){h.onresize(m)}var r=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(r);var n=r.parentNode,q=h.getOverflow(n);while(n.parentNode&&n!==document.body&&q==="visible"){n=n.parentNode;q=h.getOverflow(n)}if(q!=="visible"){l.scroll_parent=n;var p=h.getXY(n);o.x-=p.x;o.y-=p.y;p=h.getBorder(n);o.x-=p.x;o.y-=p.y}l.style.left=(-o.x)+"px";l.style.top=(-o.y)+"px";if(h.msiePositionBug){setTimeout(h.SetWH,0)}else{h.SetWH()}return o},SetWH:function(){var l=document.getElementById("MathJax_ZoomOverlay");l.style.width=l.style.height="1px";var m=l.scroll_parent||document.documentElement||document.body;l.style.width=m.scrollWidth+"px";l.style.height=Math.max(m.clientHeight,m.scrollHeight)+"px"},getOverflow:(window.getComputedStyle?function(l){return getComputedStyle(l).overflow}:function(l){return(l.currentStyle||{overflow:"visible"}).overflow}),getBorder:function(o){var m={thin:1,medium:2,thick:3};var n=(window.getComputedStyle?getComputedStyle(o):(o.currentStyle||{borderLeftWidth:0,borderTopWidth:0}));var l=n.borderLeftWidth,p=n.borderTopWidth;if(m[l]){l=m[l]}else{l=parseInt(l)}if(m[p]){p=m[p]}else{p=parseInt(p)}return{x:l,y:p}},getXY:function(o){var l=0,n=0,m;m=o;while(m.offsetParent){l+=m.offsetLeft;m=m.offsetParent}if(h.operaPositionBug){o.style.border="1px solid"}m=o;while(m.offsetParent){n+=m.offsetTop;m=m.offsetParent}if(h.operaPositionBug){o.style.border=""}return{x:l,y:n}},Remove:function(n){var p=document.getElementById("MathJax_ZoomFrame");if(p){var o=MathJax.OutputJax[p.previousSibling.jaxID];var l=o.getJaxFromMath(p.previousSibling);a.signal.Post(["math unzoomed",l]);p.parentNode.removeChild(p);p=document.getElementById("MathJax_ZoomTracker");if(p){p.parentNode.removeChild(p)}if(h.operaRefreshBug){var m=d.addElement(document.body,"div",{style:{position:"fixed",left:0,top:0,width:"100%",height:"100%",backgroundColor:"white",opacity:0},id:"MathJax_OperaDiv"});document.body.removeChild(m)}if(window.removeEventListener){removeEventListener("resize",h.Resize,false)}else{if(window.detachEvent){detachEvent("onresize",h.Resize)}else{window.onresize=h.onresize;delete h.onresize}}}return e(n)}};a.Browser.Select({MSIE:function(l){var n=(document.documentMode||0);var m=(n>=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML);
    51. 

  51. 

  52. (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:"MathJax_Menu_Close",menu:B,ontouchstart:a.Close,ontouchend:h,onmousedown:a.Close,onmouseup:h},[["img",{src:p.closeImg,style:{width:"100%",height:"100%"}}]])}this.posted=true;t.style.width=(t.offsetWidth+2)+"px";var A=s.pageX,z=s.pageY;if(!A&&!z){A=s.clientX+document.body.scrollLeft+document.documentElement.scrollLeft;z=s.clientY+document.body.scrollTop+document.documentElement.scrollTop}if(!B){if(A+t.offsetWidth>document.body.offsetWidth-this.margin){A=document.body.offsetWidth-t.offsetWidth-this.margin}if(a.isMobile){A=Math.max(5,A-Math.floor(t.offsetWidth/2));z-=20}a.skipUp=s.isContextMenu}else{var w="left",C=B.offsetWidth;A=(a.isMobile?30:C-2);z=0;while(B&&B!==r){A+=B.offsetLeft;z+=B.offsetTop;B=B.parentNode}if(A+t.offsetWidth>document.body.offsetWidth-this.margin&&!a.isMobile){w="right";A=Math.max(this.margin,A-C-t.offsetWidth+6)}if(!n){t.style["borderRadiusTop"+w]=0;t.style["WebkitBorderRadiusTop"+w]=0;t.style["MozBorderRadiusTop"+w]=0;t.style["KhtmlBorderRadiusTop"+w]=0}}t.style.left=A+"px";t.style.top=z+"px";if(document.selection&&document.selection.empty){document.selection.empty()}return h(s)},Remove:function(r,s){j.Post(["unpost",a.jax]);var t=document.getElementById("MathJax_MenuFrame");if(t){t.parentNode.removeChild(t);if(this.msieFixedPositionBug){detachEvent("onresize",a.Resize)}}if(a.jax.hover){delete a.jax.hover.nofade;d.UnHover(a.jax)}return h(r)},Find:function(r){return this.FindN(1,r,[].slice.call(arguments,1))},FindId:function(r){return this.FindN(0,r,[].slice.call(arguments,1))},FindN:function(v,s,u){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[v]===s){if(u.length){if(!this.items[t].menu){return null}return this.items[t].menu.FindN(v,u[0],u.slice(1))}return this.items[t]}}return null},IndexOf:function(r){return this.IndexOfN(1,r)},IndexOfId:function(r){return this.IndexOfN(0,r)},IndexOfN:function(u,s){for(var t=0,r=this.items.length;t<r;t++){if(this.items[t].name[u]===s){return t}}return null}},{config:p,div:null,Close:function(r){return a.Event(r,this.menu||this.parentNode,(this.menu?"Touchend":"Remove"))},Remove:function(r){return a.Event(r,this,"Remove")},Mouseover:function(r){return 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    53. 

  53. 

  54. 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    55. 

  55. 

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    57. 

  57. 

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    59. 

  59. 

  60. 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");
    61. 

  61. 

  62. 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m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m={stretchy:false},l;if(this.stack.env.font){m.mathvariant=this.stack.env.font}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var n=this.stack.Prev("nopop");if(!n||n.texClass!==h.TEXCLASS.OP){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}n.movesupsub=(l?true:false);n.movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}var m=h.munderover(o,null,null);if(l){m.movesupsub=true}m.data[m[p]]=this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p=="under")}));this.Push(m)},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ 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l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1 width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({mclass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,t,q,s,n,l,u){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(s||"1em")}});if(u){p.isCases=true}if(o||t){p.open=o;p.close=t}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"");if(p&&!p.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mo().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(p){var n=p.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},Begin:function(m){var n=this.GetArgument(m);if(n.match(/[^a-z*]/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",n])}var o=this.envFindName(n);if(!o){d.Error(["UnknownEnv","Unknown environment '%1'",n])}if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(!(o instanceof Array)){o=[o]}var l=b.begin().With({name:n,end:o[1],parse:this});if(o[0]&&this[o[0]]){l=this[o[0]].apply(this,[l].concat(o.slice(2)))}this.Push(l)},End:function(l){this.Push(b.end().With({name:this.GetArgument(l)}))},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":o++;break;case"}":if(o==0){d.Error(["ExtraClose","Extra close brace"])}if(--o==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBrace","Missing close brace"]);break}return this.string.charAt(this.i++)},GetBrackets:function(m,o){if(this.GetNext()!="["){return o}var l=++this.i,n=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":n++;break;case"\\":this.i++;break;case"}":if(n--<=0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"])}break;case"]":if(n==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",m])},GetDelimiter:function(l){while(this.nextIsSpace()){this.i++}var m=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(m=="\\"){m+=this.GetCS(l)}if(f.delimiter[m]!=null){return this.convertDelimiter(m)}}d.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",l])},GetDimen:function(m){var n;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){n=this.GetArgument(m);if(n.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return n.replace(/ /g,"")}}else{n=this.string.slice(this.i);var l=n.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(l){this.i+=l[0].length;return l[1].replace(/ /g,"")}}d.Error(["MissingDimOrUnits","Missing dimension or its units for %1",m])},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1",o])}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",o,n])},ParseArg:function(l){return d.Parse(this.GetArgument(l),this.stack.env).mml()},ParseUpTo:function(l,m){return d.Parse(this.GetUpTo(l,m),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:false};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-1),{}).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="}"&&n==="}"){m.push(h.TeXAtom(d.Parse(q.slice(l,o),{}).mml().With(p)));n="";l=o}else{if(r==="\\"){if(n===""&&q.substr(o).match(/^(eq)?ref\s*\{/)){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="}";l=o-1}else{r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-2),{}).mml().With(p)));n="";l=o}else{if(r==="$"&&n===""){o--;q=q.substr(0,o-1)+q.substr(o)}}}}}}}}if(n!==""){d.Error(["MathNotTerminated","Math not terminated in text box"])}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(m,l){m=m.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(m)).With(l)},SubstituteArgs:function(m,l){var p="";var o="";var q;var n=0;while(n<l.length){q=l.charAt(n++);if(q==="\\"){p+=q+l.charAt(n++)}else{if(q==="#"){q=l.charAt(n++);if(q==="#"){p+=q}else{if(!q.match(/[1-9]/)||q>m.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}o=this.AddArgs(this.AddArgs(o,p),m[q-1]);p=""}}else{p+=q}}}return this.AddArgs(o,p)},AddArgs:function(m,l){if(l.match(/^[a-z]/i)&&m.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){m+=" "}if(m.length+l.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return m+l}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:k,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(l){var m,n=false,p=MathJax.HTML.getScript(l);var r=(l.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var q={math:p,display:r,script:l};this.prefilterHooks.Execute(q);p=q.math;try{m=d.Parse(p).mml()}catch(o){if(!o.texError){throw o}m=this.formatError(o,p,r,l);n=true}if(m.inferred){m=h.apply(MathJax.ElementJax,m.data)}else{m=h(m)}if(r){m.root.display="block"}if(n){m.texError=true}q.math=m;this.postfilterHooks.Execute(q);return q.math},prefilterMath:function(m,n,l){return m},postfilterMath:function(m,n,l){this.combineRelations(m.root);return m},formatError:function(o,n,p,l){var m=o.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",m,n,p,l]);return h.merror(m)},Error:function(l){if(l instanceof Array){l=j.apply(j,l)}throw c.Insert(Error(l),{texError:true})},Macro:function(l,m,n){f.macros[l]=["Macro"].concat([].slice.call(arguments,1));f.macros[l].isUser=true},fenced:function(n,m,o){var l=h.mrow();l.open=n;l.close=o;if(n){l.Append(h.mo(n).With({fence:true,stretchy:true,texClass:h.TEXCLASS.OPEN}))}if(m.type==="mrow"){l.Append.apply(l,m.data)}else{l.Append(m)}if(o){l.Append(h.mo(o).With({fence:true,stretchy:true,texClass:h.TEXCLASS.CLOSE}))}return l},combineRelations:function(p){var q,l,o,n;for(q=0,l=p.data.length;q<l;q++){if(p.data[q]){if(p.isa(h.mrow)){while(q+1<l&&(o=p.data[q])&&(n=p.data[q+1])&&o.isa(h.mo)&&n.isa(h.mo)&&o.Get("texClass")===h.TEXCLASS.REL&&n.Get("texClass")===h.TEXCLASS.REL){if(o.variantForm==n.variantForm&&o.Get("mathvariant")==n.Get("mathvariant")&&o.style==n.style&&o["class"]==n["class"]&&!o.id&&!n.id){o.Append.apply(o,n.data);p.data.splice(q+1,1);l--}else{o.rspace=n.lspace="0pt";q++}}}if(!p.data[q].isToken){this.combineRelations(p.data[q])}}}}});d.prefilterHooks.Add(function(l){l.math=d.prefilterMath(l.math,l.display,l.script)});d.postfilterHooks.Add(function(l){l.math=d.postfilterMath(l.math,l.display,l.script)});d.loadComplete("jax.js")})(MathJax.InputJax.TeX,MathJax.Hub,MathJax.Ajax);
    63. 

  63. 

  64. MathJax.Extension["TeX/AMSmath"]={version:"2.2",number:0,startNumber:0,labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("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&thinsp;lim"],projlim:["NamedOp","proj&thinsp;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.refUpdate}var h=k;if(l){h=a.formatTag(h)}if(a.useLabelIds){k=i}this.Push(b.mrow.apply(b,this.InternalMath(h)).With({href:a.formatURL(a.formatID(k)),"class":"MathJax_ref"}))},HandleDeclareOp:function(i){var h=(this.GetStar()?"\\limits":"");var j=this.trimSpaces(this.GetArgument(i));if(j.charAt(0)=="\\"){j=j.substr(1)}var k=this.GetArgument(i);k=k.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");g.Definitions.macros[j]=["Macro","\\mathop{\\rm "+k+"}"+h]},HandleOperatorName:function(i){var h=(this.GetStar()?"\\limits":"\\nolimits");var j=this.trimSpaces(this.GetArgument(i));j=j.replace(/\*/g,"\\text{*}").replace(/-/g,"\\text{-}");this.string="\\mathop{\\rm "+j+"}"+h+" "+this.string.slice(this.i);this.i=0},HandleShove:function(i,h){var j=this.stack.Top();if(j.type!=="multline"||j.data.length){g.Error(["CommandAtTheBeginingOfLine","%1 must come at the beginning of the line",i])}j.data.shove=h},CFrac:function(k){var h=this.trimSpaces(this.GetBrackets(k,"")),j=this.GetArgument(k),l=this.GetArgument(k);var i=b.mfrac(g.Parse("\\strut\\textstyle{"+j+"}",this.stack.env).mml(),g.Parse("\\strut\\textstyle{"+l+"}",this.stack.env).mml());h=({l:b.ALIGN.LEFT,r:b.ALIGN.RIGHT,"":""})[h];if(h==null){g.Error(["IllegalAlign","Illegal alignment specified in %1",k])}if(h){i.numalign=i.denomalign=h}this.Push(i)},Genfrac:function(i,k,p,m,h){if(k==null){k=this.GetDelimiterArg(i)}else{k=this.convertDelimiter(k)}if(p==null){p=this.GetDelimiterArg(i)}else{p=this.convertDelimiter(p)}if(m==null){m=this.GetArgument(i)}if(h==null){h=this.trimSpaces(this.GetArgument(i))}var l=this.ParseArg(i);var o=this.ParseArg(i);var j=b.mfrac(l,o);if(m!==""){j.linethickness=m}if(k||p){j=g.fenced(k,j,p)}if(h!==""){var n=(["D","T","S","SS"])[h];if(n==null){g.Error(["BadMathStyleFor","Bad math style for %1",i])}j=b.mstyle(j);if(n==="D"){j.displaystyle=true;j.scriptlevel=0}else{j.displaystyle=false;j.scriptlevel=h-1}}this.Push(j)},Multline:function(i,h){this.Push(i);this.checkEqnEnv();return e.multline(h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",width:g.config.MultLineWidth,columnwidth:"100%",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AMSarray:function(j,i,h,l,k){this.Push(j);if(h){this.checkEqnEnv()}l=l.replace(/[^clr]/g,"").split("").join(" ");l=l.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");return e.AMSarray(j.name,i,h,this.stack).With({arraydef:{displaystyle:true,rowspacing:".5em",columnalign:l,columnspacing:(k||"1em"),rowspacing:"3pt",side:g.config.TagSide,minlabelspacing:g.config.TagIndent}})},AlignAt:function(k,i,h){var p,j,o="",m=[];if(!h){j=this.GetBrackets("\\begin{"+k.name+"}")}p=this.GetArgument("\\begin{"+k.name+"}");if(p.match(/[^0-9]/)){g.Error(["PositiveIntegerArg","Argument to %1 must me a positive integer","\\begin{"+k.name+"}"])}while(p>0){o+="rl";m.push("0em 0em");p--}m=m.join(" ");if(h){return this.AMSarray(k,i,h,o,m)}var l=this.Array.call(this,k,null,null,o,m,".5em","D");return this.setArrayAlign(l,j)},EquationBegin:function(h,i){this.checkEqnEnv();this.stack.global.forcetag=(i&&a.autoNumber!=="none");return h},EquationStar:function(h,i){this.stack.global.tagged=true;return i},checkEqnEnv:function(){if(this.stack.global.eqnenv){g.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(h,l){var k=this.GetNext();if(k==="\\"){var j=this.i;k=this.GetArgument(h);this.i=j;if(k==="\\limits"){if(h==="\\idotsint"){l="\\!\\!\\mathop{\\,\\,"+l+"}"}else{l="\\!\\!\\!\\mathop{\\,\\,\\,"+l+"}"}}}this.string=l+" "+this.string.slice(this.i);this.i=0},xArrow:function(j,n,m,h){var k={width:"+"+(m+h)+"mu",lspace:m+"mu"};var o=this.GetBrackets(j),p=this.ParseArg(j);var q=b.mo(b.chars(String.fromCharCode(n))).With({stretchy:true,texClass:b.TEXCLASS.REL});var i=b.munderover(q);i.SetData(i.over,b.mpadded(p).With(k).With({voffset:".15em"}));if(o){o=g.Parse(o,this.stack.env).mml();i.SetData(i.under,b.mpadded(o).With(k).With({voffset:"-.24em"}))}this.Push(i)},GetDelimiterArg:function(h){var i=this.trimSpaces(this.GetArgument(h));if(i==""){return null}if(d.delimiter[i]==null){g.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",h])}return this.convertDelimiter(i)},GetStar:function(){var h=(this.GetNext()==="*");if(h){this.i++}return h}});e.Augment({autoTag:function(){var i=this.global;if(!i.notag){f.number++;i.tagID=a.formatNumber(f.number.toString());var h=g.Parse("\\text{"+a.formatTag(i.tagID)+"}",{}).mml();i.tag=b.mtd(h.With({id:a.formatID(i.tagID)}))}},getTag:function(){var i=this.global,h=i.tag;i.tagged=true;if(i.label){f.eqlabels[i.label]=i.tagID;if(a.useLabelIds){h.id=a.formatID(i.label)}}delete i.tag;delete i.tagID;delete i.label;return h}});e.multline=e.array.Subclass({type:"multline",Init:function(i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(i&&a.autoNumber!=="none");this.save={notag:h.global.notag};h.global.tagged=!i&&!h.global.forcetag},EndEntry:function(){var h=b.mtd.apply(b,this.data);if(this.data.shove){h.columnalign=this.data.shove}this.row.push(h);this.data=[]},EndRow:function(){if(this.row.length!=1){g.Error(["MultlineRowsOneCol","The rows within the %1 environment must have exactly one column","multline"])}this.table.push(this.row);this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);if(this.table.length){var j=this.table.length-1,l,k=-1;if(!this.table[0][0].columnalign){this.table[0][0].columnalign=b.ALIGN.LEFT}if(!this.table[j][0].columnalign){this.table[j][0].columnalign=b.ALIGN.RIGHT}if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){k=(this.arraydef.side==="left"?0:this.table.length-1);this.table[k]=[this.getTag()].concat(this.table[k])}for(l=0,j=this.table.length;l<j;l++){var h=(l===k?b.mlabeledtr:b.mtr);this.table[l]=h.apply(b,this.table[l])}}this.global.notag=this.save.notag}});e.AMSarray=e.array.Subclass({type:"AMSarray",Init:function(k,j,i,h){this.SUPER(arguments).Init.apply(this);this.numbered=(j&&a.autoNumber!=="none");this.save={notags:h.global.notags,notag:h.global.notag};h.global.notags=(i?null:k);h.global.tagged=!j&&!h.global.forcetag},EndRow:function(){var h=b.mtr;if(!this.global.tag&&this.numbered){this.autoTag()}if(this.global.tag&&!this.global.notags){this.row=[this.getTag()].concat(this.row);h=b.mlabeledtr}if(this.numbered){delete this.global.notag}this.table.push(h.apply(b,this.row));this.row=[]},EndTable:function(){this.SUPER(arguments).EndTable.call(this);this.global.notags=this.save.notags;this.global.notag=this.save.notag}});e.start.Augment({oldCheckItem:e.start.prototype.checkItem,checkItem:function(j){if(j.type==="stop"){var h=this.mmlData(),i=this.global;if(f.display&&!i.tag&&!i.tagged&&!i.isInner&&(a.autoNumber==="all"||i.forcetag)){this.autoTag()}if(i.tag){var l=[this.getTag(),b.mtd(h)];var k={side:g.config.TagSide,minlabelspacing:g.config.TagIndent,columnalign:h.displayAlign};if(h.displayAlign===b.INDENTALIGN.LEFT){k.width="100%";if(h.displayIndent&&!String(h.displayIndent).match(/^0+(\.0*)?($|[a-z%])/)){k.columnwidth=h.displayIndent+" 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j=0,h=f.refs.length;j<h;j++){f.refs[j].MathJax.state=MathJax.ElementJax.STATE.UPDATE}return MathJax.Hub.processInput({scripts:f.refs,start:new Date().getTime(),i:0,j:0,jax:{},jaxIDs:[]})}return null});g.resetEquationNumbers=function(i,h){f.startNumber=(i||0);if(!h){f.labels={}}};MathJax.Hub.Startup.signal.Post("TeX AMSmath Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSmath.js");
    65. 

  65. 

  66. 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",ntrianglerighteq:"22ED",nsubseteq:"2288",nsupseteq:"2289",nsubseteqq:["2288",{variantForm:true}],nsupseteqq:["2289",{variantForm:true}],subsetneq:"228A",supsetneq:"228B",varsubsetneq:["228A",{variantForm:true}],varsupsetneq:["228B",{variantForm:true}],subsetneqq:"2ACB",supsetneqq:"2ACC",varsubsetneqq:["2ACB",{variantForm:true}],varsupsetneqq:["2ACC",{variantForm:true}],leftleftarrows:"21C7",rightrightarrows:"21C9",leftrightarrows:"21C6",rightleftarrows:"21C4",Lleftarrow:"21DA",Rrightarrow:"21DB",twoheadleftarrow:"219E",twoheadrightarrow:"21A0",leftarrowtail:"21A2",rightarrowtail:"21A3",looparrowleft:"21AB",looparrowright:"21AC",leftrightharpoons:"21CB",rightleftharpoons:["21CC",{variantForm:true}],curvearrowleft:"21B6",curvearrowright:"21B7",circlearrowleft:"21BA",circlearrowright:"21BB",Lsh:"21B0",Rsh:"21B1",upuparrows:"21C8",downdownarrows:"21CA",upharpoonleft:"21BF",upharpoonright:"21BE",downharpoonleft:"21C3",restriction:"21BE",multimap:"22B8",downharpoonright:"21C2",leftrightsquigarrow:"21AD",rightsquigar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c=a.mo.OPTYPES.REL;MathJax.Hub.Insert(a.mo.prototype,{OPTABLE:{infix:{"\u2322":c,"\u2323":c,"\u25B3":c,"\uE006":c,"\uE007":c,"\uE00C":c,"\uE00D":c,"\uE00E":c,"\uE00F":c,"\uE010":c,"\uE011":c,"\uE016":c,"\uE017":c,"\uE018":c,"\uE019":c,"\uE01A":c,"\uE01B":c,"\uE04B":c,"\uE04F":c}}});MathJax.Hub.Startup.signal.Post("TeX AMSsymbols Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMSsymbols.js");
    67. 

  67. 

  68. (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(e){this.Parse(e)},Parse:function(g){var h;if(typeof g!=="string"){h=g.parentNode}else{h=c.ParseXML(this.preProcessMath.call(this,g));if(h==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var f=h.getElementsByTagName("parsererror")[0];if(f){c.Error(["ParsingError","Error parsing MathML: %1",f.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(h.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(h.firstChild.nodeName.toLowerCase()==="html"){var e=h.getElementsByTagName("h1")[0];if(e&&e.textContent==="XML parsing error"&&e.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(e.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(h.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a <math> element, not %1","<"+h.firstChild.nodeName+">"])}this.mml=this.MakeMML(h.firstChild)},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])}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - 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    69. 

  69. 

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l=this.getValues("displaystyle","accent","accentunder","align");if(!l.displaystyle&&this.data[this.base]!=null&&this.data[this.base].CoreMO().Get("movablelimits")){return g.msubsup.prototype.toSVG.call(this)}var E=this.SVG();this.SVGhandleSpace(E);var M=E.scale=this.SVGgetScale();var p=[],K=[],u,J,G,n=-a.BIGDIMEN,I=n;for(J=0,G=this.data.length;J<G;J++){if(this.data[J]!=null){if(J==this.base){p[J]=this.SVGdataStretched(J,F,C);K[J]=(C!=null||F==null)&&this.data[J].SVGcanStretch("Horizontal")}else{p[J]=this.data[J].toSVG();K[J]=this.data[J].SVGcanStretch("Horizontal")}if(p[J].w>I){I=p[J].w}if(!K[J]&&I>n){n=I}}}if(C==null&&F!=null){n=F}else{if(n==-a.BIGDIMEN){n=I}}for(J=I=0,G=this.data.length;J<G;J++){if(this.data[J]){if(K[J]){p[J]=this.data[J].SVGstretchH(n)}if(p[J].w>I){I=p[J].w}}}var B=a.TeX.rule_thickness;var o=p[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,scale:M};var s,q,w,v,r,A,H,L=0;if(o.ic){L=1.3*o.ic+0.05}for(J=0,G=this.data.length;J<G;J++){if(this.data[J]!=null){u=p[J];r=a.TeX.big_op_spacing5*M;var z=(J!=this.base&&l[this.ACCENTS[J]]);if(z&&u.w<=1){u.x=-u.l;p[J]=i.G().With({removeable:false});p[J].Add(u);p[J].Clean();p[J].w=-u.l;u=p[J]}A={left:0,center:(I-u.w)/2,right:I-u.w}[l.align];s=A;q=0;if(J==this.over){if(z){H=B*M;r=0;if(o.skew){s+=o.skew}}else{w=a.TeX.big_op_spacing1*M;v=a.TeX.big_op_spacing3*M;H=Math.max(w,v-Math.max(0,u.d))}H=Math.max(H,1500/a.em);s+=L/2;q=o.h+u.d+H;u.h+=r;if(u.h>u.H){u.H=u.h}}else{if(J==this.under){if(z){H=3*B*M;r=0}else{w=a.TeX.big_op_spacing2*M;v=a.TeX.big_op_spacing4*M;H=Math.max(w,v-u.h)}H=Math.max(H,1500/a.em);s-=L/2;q=-(o.d+u.h+H);u.d+=r;if(u.d>u.D){u.D=u.d}}}E.Add(u,s,q)}}E.Clean();this.SVGhandleColor(E);this.SVGsaveData(E);return E}});g.msubsup.Augment({toSVG:function(G,z){this.SVGgetStyles();var B=this.SVG();this.SVGhandleSpace(B);var K=B.scale=this.SVGgetScale(),E=this.SVGgetMu(B);var m=B.Add(this.SVGdataStretched(this.base,G,z));var l=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var I=a.TeX.x_height*K,y=a.TeX.scriptspace*K;var k,n;if(this.SVGnotEmpty(this.data[this.sup])){k=this.data[this.sup].toSVG();k.w+=y;k.r=Math.max(k.w,k.r)}if(this.SVGnotEmpty(this.data[this.sub])){n=this.data[this.sub].toSVG();n.w+=y;n.r=Math.max(n.w,n.r)}var C=a.TeX.sup_drop*l,A=a.TeX.sub_drop*l;var w=m.h+(m.y||0)-C,o=m.d-(m.y||0)+A,J=0,F;if(m.ic){m.w-=m.ic;J=1.3*m.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(this.data[this.base].data.join("").length===1&&m.scale===1&&!m.stretched&&!this.data[this.base].Get("largeop")){w=o=0}}var H=this.getValues("subscriptshift","superscriptshift");H.subscriptshift=(H.subscriptshift===""?0:a.length2em(H.subscriptshift,E));H.superscriptshift=(H.superscriptshift===""?0:a.length2em(H.superscriptshift,E));if(!k){if(n){o=Math.max(o,a.TeX.sub1*K,n.h-(4/5)*I,H.subscriptshift);B.Add(n,m.w,-o);this.data[this.sub].SVGdata.dy=-o}}else{if(!n){values=this.getValues("displaystyle","texprimestyle");F=a.TeX[(values.displaystyle?"sup1":(values.texprimestyle?"sup3":"sup2"))];w=Math.max(w,F*K,k.d+(1/4)*I,H.superscriptshift);B.Add(k,m.w+J,w);this.data[this.sup].SVGdata.dx=J;this.data[this.sup].SVGdata.dy=w}else{o=Math.max(o,a.TeX.sub2*K);var x=a.TeX.rule_thickness*K;if((w-k.d)-(n.h-o)<3*x){o=3*x-w+k.d+n.h;C=(4/5)*I-(w-k.d);if(C>0){w+=C;o-=C}}B.Add(k,m.w+J,Math.max(w,H.superscriptshift));B.Add(n,m.w,-Math.max(o,H.subscriptshift));this.data[this.sup].SVGdata.dx=J;this.data[this.sup].SVGdata.dy=Math.max(w,H.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(o,H.subscriptshift)}}B.Clean();this.SVGhandleColor(B);this.SVGsaveData(B);return B}});g.mmultiscripts.Augment({toSVG:g.mbase.SVGautoload});g.mtable.Augment({toSVG:g.mbase.SVGautoload});g["annotation-xml"].Augment({toSVG:g.mbase.SVGautoload});g.math.Augment({SVG:i.Subclass({type:"svg",removeable:false}),toSVG:function(t,m){if(this.data[0]){this.SVGgetStyles();g.mbase.prototype.displayAlign=c.config.displayAlign;g.mbase.prototype.displayIndent=c.config.displayIndent;var q=i.G({stroke:"black",fill:"black","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"}).With({removeable:false});q.Add(this.data[0].toSVG(),0,0,true);q.Clean();this.SVGhandleColor(q);var s=this.SVG();s.element.setAttribute("xmlns:xlink",j);s.Add(q);s.Clean();this.SVGsaveData(s);var p=Math.max(-s.l,0),k=Math.max(s.r-s.w,0);var n=s.element.style;n.width=a.Ex(p+s.w+k);n.height=a.Ex(s.H+s.D+2*a.em);n.verticalAlign=a.Ex(-s.D-3*a.em);n.marginLeft=a.Ex(-p);n.marginRight=a.Ex(-k);s.element.setAttribute("viewBox",(-p)+" "+(-s.H-a.em)+" "+(p+s.w+k)+" "+(s.H+s.D+2*a.em));s.element.style.margin="1px 0px";if(s.H>s.h||s.D>s.d){var o=e.Element("span",{style:{display:"inline-block","white-space":"nowrap",padding:"1px 0px"},isMathJax:true},[["span",{style:{display:"inline-block",position:"relative",isMathJax:true,width:a.Ex(s.w),height:a.Ex(s.h+s.d),"vertical-align":a.Ex(-s.d)}}]]);o.firstChild.appendChild(s.element);s.element=o;n.verticalAlign=n.margin="";n.position="absolute";n.bottom=a.Ex(s.d-s.D);n.left=0}t.appendChild(s.element);s.element=null;if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==g.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===g.INDENTALIGN.AUTO){u.indentalign=this.displayAlign}m.style.textAlign=u.indentalign;if(u.indentshiftfirst!==g.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift=this.displayIndent}if(u.indentshift&&u.indentalign!==g.INDENTALIGN.CENTER&&!s.hasIndent){t.style[{left:"marginLeft",right:"marginRight"}[u.indentalign]]=a.Ex(a.length2em(u.indentshift))}}}return t}});g.TeXAtom.Augment({toSVG:function(){this.SVGgetStyles();var k=this.SVG();this.SVGhandleSpace(k);if(this.data[0]!=null){var l=this.data[0].toSVG(),m=0;if(this.texClass===g.TEXCLASS.VCENTER){m=a.TeX.axis_height-(l.h+l.d)/2+l.d}k.Add(l,0,m);k.ic=l.ic}this.SVGhandleColor(k);this.SVGsaveData(k);return 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    71. 

  71. 

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ai=ak(aI.columnspacing),Q=ak(aI.rowspacing),af=ak(aI.columnalign),I=ak(aI.rowalign),K=ak(aI.columnlines),g=ak(aI.rowlines),an=ak(aI.columnwidth),ar=[];for(aD=0,aA=ai.length;aD<aA;aD++){ai[aD]=d.length2em(ai[aD],t)}for(aD=0,aA=Q.length;aD<aA;aD++){Q[aD]=d.length2em(Q[aD],t)}while(ai.length<u){ai.push(ai[ai.length-1])}while(af.length<=u){af.push(af[af.length-1])}while(K.length<u){K.push(K[K.length-1])}while(an.length<=u){an.push(an[an.length-1])}while(Q.length<L.length){Q.push(Q[Q.length-1])}while(I.length<=L.length){I.push(I[I.length-1])}while(g.length<L.length){g.push(g[g.length-1])}if(G[aF]){af[aF]=(aI.side.substr(0,1)==="l"?"left":"right");ai[aF]=-h[aF]}for(aD=0,aA=L.length;aD<aA;aD++){O=this.data[aD];ar[aD]=[];if(O.rowalign){I[aD]=O.rowalign}if(O.columnalign){ar[aD]=ak(O.columnalign);while(ar[aD].length<=u){ar[aD].push(ar[aD][ar[aD].length-1])}}}if(aI.equalrows){var R=Math.max.apply(Math,v),am=Math.max.apply(Math,E);for(aD=0,aA=L.length;aD<aA;aD++){av=((R+am)-(v[aD]+E[aD]))/2;v[aD]+=av;E[aD]+=av}}aw=v[0]+E[L.length-1];for(aD=0,aA=L.length-1;aD<aA;aD++){aw+=Math.max((v[aD]+E[aD]?aK:0),E[aD]+v[aD+1]+Q[aD])}var ab=0,X=0,ax,aG=aw;if(aI.frame!=="none"||(aI.columnlines+aI.rowlines).match(/solid|dashed/)){var q=ak(aI.framespacing);if(q.length!=2){q=ak(this.defaults.framespacing)}ab=d.length2em(q[0],t);X=d.length2em(q[1],t);aG=aw+2*X}var e,au,az="";if(typeof(aI.align)!=="string"){aI.align=String(aI.align)}if(aI.align.match(/(top|bottom|center|baseline|axis)( +(-?\d+))?/)){az=RegExp.$3;aI.align=RegExp.$1}else{aI.align=this.defaults.align}if(az!==""){az=parseInt(az);if(az<0){az=L.length+1+az}if(az<1){az=1}else{if(az>L.length){az=L.length}}e=0;au=-(aw+X)+v[0];for(aD=0,aA=az-1;aD<aA;aD++){var 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  74. MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_SVG-full.js");
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