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jax.js

jax.js 26 KB
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  1. /*
    2. 

  2.  *  /MathJax/jax/output/NativeMML/jax.js
    3. 

  3.  *
    4. 

  4.  *  Copyright (c) 2009-2015 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Licensed under the Apache License, Version 2.0 (the "License");
    7. 

  7.  *  you may not use this file except in compliance with the License.
    8. 

  8.  *  You may obtain a copy of the License at
    9. 

  9.  *
    10. 

  10.  *      http://www.apache.org/licenses/LICENSE-2.0
    11. 

  11.  *
    12. 

  12.  *  Unless required by applicable law or agreed to in writing, software
    13. 

  13.  *  distributed under the License is distributed on an "AS IS" BASIS,
    14. 

  14.  *  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    15. 

  15.  *  See the License for the specific language governing permissions and
    16. 

  16.  *  limitations under the License.
    17. 

  17.  */
    18. 

  18. 

  19. (function(l,c,g,e){var f,i=c.Browser.isMSIE;var h,b,d,k;c.Register.StartupHook("MathZoom Ready",function(){k=MathJax.Extension.MathZoom});var j=function(m,o){var n=e.Element("span");m="padding"+m;if(o){n.style.cssText=(o.getAttribute("style")||"");if(n.style.padding===""&&(n.style[m]||"")===""){n.style[m]="0px";o.setAttribute("style",n.style.cssText)}}};var a=function(r,m,p){if(r){var o=e.Element("span");o.style.cssText=(r.getAttribute("style")||"");if(o.style.padding===""){var q={paddingLeft:p,paddingTop:m,paddingRight:"0px",paddingBottom:"0px"};for(var n in q){if(q.hasOwnProperty(n)){if((o.style[n]||"")===""){o.style[n]=q[n]}}}}r.setAttribute("style",o.style.cssText)}};l.Augment({config:{styles:{".MathJax_MathML":{"font-style":"normal","font-weight":"normal","line-height":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-align":"left","text-transform":"none","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none",direction:"ltr","max-width":"none","max-height":"none","min-width":0,"min-height":0,border:0,padding:0,margin:0},"span.MathJax_MathML":{display:"inline!important"},"div.MathJax_MathML":{display:"block!important"},".MathJax_mmlExBox":{display:"block!important",overflow:"hidden",height:"1px",width:"60ex","min-height":0,"max-height":"none",padding:0,border:0,margin:0}}},handlesVariants:false,settings:c.config.menuSettings,ex:1,scale:1,adjustWidths:[],Config:function(){this.SUPER(arguments).Config.call(this);if(this.settings.scale){this.config.scale=this.settings.scale}if(c.config.displayAlign!=="center"){var o=c.config.displayAlign,m=c.config.displayIndent;var n={"text-align":o+"!important"};n["margin-"+o]=m+"!important";c.Insert(this.config.styles,{"div.MathJax_MathML":n,"div.MathJax_MathML math":{"text-align":o},"div.MathJax_MathContainer > span":{"text-align":o+"!important"}})}if(!this.require){this.require=[]}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){h=MathJax.Extension.MathEvents.Event;b=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=h.ContextMenu;this.Mousedown=h.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;if(!c.Browser.hasMathPlayer){this.EmExSpan=e.Element("span",{style:{position:"absolute","font-size-adjust":"none"}},[["div",{className:"MathJax_mmlExBox"}],["span",{className:"MathJax_MathML"}]]);f.math(f.mspace().With({width:"60ex"})).toNativeMML(this.EmExSpan.lastChild)}return g.Styles(this.config.styles)},InitializeMML:function(){this.initialized=true;if(c.Browser.hasMathPlayer){try{if(!c.Browser.mpNamespace){var m=document.createElement("object");m.id="mathplayer";m.classid="clsid:32F66A20-7614-11D4-BD11-00104BD3F987";document.getElementsByTagName("head")[0].appendChild(m);document.namespaces.add("m","http://www.w3.org/1998/Math/MathML");c.Browser.mpNamespace=true}if(!c.Browser.mpImported){document.namespaces.m.doImport("#mathplayer");c.Browser.mpImported=true}}catch(n){if(!this.config.noMathPlayerWarning){alert(MathJax.Localization._(["MathML","MathPlayer"],"MathJax was not able to set up MathPlayer.\n\nIf MathPlayer is not installed, you need to install it first.\nOtherwise, your security settings may be preventing ActiveX     \ncontrols from running.  Use the Internet Options item under\nthe Tools menu and select the Security tab, then press the\nCustom Level button. Check that the settings for\n'Run ActiveX Controls', and 'Binary and script behaviors'\nare enabled.\n\nCurrently you will see error messages rather than\ntypeset mathematics."))}}}else{document.body.appendChild(this.EmExSpan);this.defaultEx=this.EmExSpan.firstChild.offsetWidth/60;this.defaultMEx=this.EmExSpan.lastChild.offsetWidth/60;document.body.removeChild(this.EmExSpan)}},preTranslate:function(o){var t=o.jax[this.id],u,p=t.length,y,r,A,w,z,n,v,s,q;for(u=0;u<p;u++){y=t[u];if(!y.parentNode){continue}if(!this.initialized){this.InitializeMML()}r=y.previousSibling;if(r&&r.className==="MathJax_MathML"){r.parentNode.removeChild(r)}n=y.MathJax.elementJax;if(!n){continue}z=n.root;n.NativeMML={};var x=(z.Get("display")==="block"?"div":"span");A=e.Element(x,{className:"MathJax_MathML",id:n.inputID+"-Frame"},[["span",{className:"MathJax_MathContainer",isMathJax:true,jaxID:this.id,style:{position:"relative",display:"inline-block","white-space":"nowrap"}},[["span",{isMathJax:true,style:{display:"inline-block"}}]]]]);y.parentNode.insertBefore(A,y);if(!i){y.parentNode.insertBefore(this.EmExSpan.cloneNode(true),y)}}for(u=0;u<p;u++){y=t[u];if(!y.parentNode){continue}n=y.MathJax.elementJax;if(!n){continue}if(!i){w=y.previousSibling;v=w.firstChild.offsetWidth/60;s=w.lastChild.offsetWidth/60;if(v===0||v==="NaN"){v=this.defaultEx;s=this.defaultMEx}q=(this.config.matchFontHeight&&s>1?v/s:1);q=Math.floor(Math.max(this.config.minScaleAdjust/100,q)*this.config.scale);n.NativeMML.ex=v;n.NativeMML.mex=s}else{q=100}n.NativeMML.fontSize=q+"%";n.NativeMML.scale=q/100}if(!i){for(u=0;u<p;u++){y=t[u];if(y.parentNode&&y.MathJax.elementJax){y.parentNode.removeChild(y.previousSibling)}}}},Translate:function(s){if(!s.parentNode){return}var m=s.MathJax.elementJax,t=m.root;var u=document.getElementById(m.inputID+"-Frame");if(!u){return}var n=u.firstChild,q=n.firstChild;this.ex=m.NativeMML.ex||this.defaultEx;this.scale=m.NativeMML.scale||1;if(this.scale!==1){u.style.fontSize=m.NativeMML.fontSize}try{t.toNativeMML(q,m)}catch(r){if(r.restart){while(q.firstChild){q.removeChild(q.firstChild)}}throw r}if(i){if(n.addEventListener){for(var o in this.MSIE9events){if(this.MSIE9events.hasOwnProperty(o)){n.addEventListener(o,this.MSIE9event,true)}}}else{var p=(this.config.showMathMenuMSIE!=null?this:c).config;if(p.showMathMenuMSIE&&!this.settings.mpContext&&!this.settings.mpMouse){this.MSIEoverlay(n)}else{n.style.position="";q.firstChild.onmousedown=this.MSIEaltMenu}}}else{n.oncontextmenu=h.Menu;n.onmouseover=h.Mouseover;n.onmouseout=h.Mouseout;n.onmousedown=h.Mousedown;n.onclick=h.Click;n.ondblclick=h.DblClick;if(c.Browser.noContextMenu){n.ontouchstart=b.start;n.ontouchend=b.end}}},postTranslate:function(n){if(this.forceReflow){var m=(document.styleSheets||[])[0]||{};m.disabled=true;m.disabled=false}},Remove:function(m){var n=m.SourceElement();if(!n){return}n=n.previousSibling;if(!n){return}if(n.className.match(/MathJax_MathML/)){n.parentNode.removeChild(n)}},MMLnamespace:"http://www.w3.org/1998/Math/MathML",isFullWidth:function(r){if(!r){return}var q=r.getAttribute("width")||(String(r.getAttribute("style")).match(/(?:^| )width: *([^; ]*)/)||[])[1];if(q){return !!q.match(/%/)}if(r.nodeName.match(/^(semantics|math|mstyle)$/)){q=this.isFullWidth(r.firstChild)}else{if(r.nodeName.toLowerCase()==="mrow"){for(var o=0,n=r.childNodes.length;o<n&&!q;o++){q=this.isFullWidth(r.childNodes[o])}}}if(q){var p="width:100%; "+(r.getAttribute("style")||"");r.setAttribute("style",p.replace(/ +$/,""))}return q},MSIEoverlay:function(m){var n=m.firstChild;if(n.nodeName.toLowerCase()==="span"){n=n.firstChild}var o=this.getHoverBBox(null,n,{});e.addElement(m,"span",{style:{display:"inline-block",width:0,height:0,position:"relative"}},[["span",{isMathJax:true,className:"MathJax_MathPlayer_Overlay",style:{display:"inline-block",position:"absolute",left:d.Px(-o.w),top:d.Px(-o.h-(o.y||0)-1),width:d.Px(o.w),height:d.Px(o.h+o.d),cursor:"pointer","background-color":"white",filter:"alpha(opacity=0)"}}]]);c.Insert(m,{msieMath:n,onmousedown:this.MSIEevent,oncontextmenu:this.MSIEevent,onclick:this.MSIEevent,onmouseup:this.MSIEevent,onmousemove:this.MSIEevent,ondblclick:this.MSIEevent,onmouseover:this.MSIEevent,onmouseout:this.MSIEevent})},MSIEevents:{mousedown:"Mousedown",contextmenu:"ContextMenu",click:"Click",mouseup:"Mouseup",mousemove:"Mousemove",dblclick:"DblClick",mouseover:"Mouseover",mouseout:"Mouseout"},MSIEevent:function(){var n=window.event;var m=l.MSIEevents[n.type];if(l[m]&&l[m](n,this)===false){return false}if(k&&k.HandleEvent(n,m,this)===false){return false}if(n.srcElement.className==="MathJax_MathPlayer_Overlay"&&this.msieMath.fireEvent){if(m==="ContextMenu"||m==="Mouseover"||m==="Mouseout"){this.msieMath.fireEvent("on"+n.type,n)}}return h.False(n)},MSIEaltMenu:function(){var m=this.parentNode.parentNode;while(!m.jaxID){m=m.parentNode}h.AltContextMenu(window.event,m)},MSIE9events:{contextmenu:"Menu",click:"Click",dblclick:"DblClick",mouseup:"False",mouseover:"Mouseover",mouseout:"Mouseout"},MSIE9event:function(n){if(n.type==="contextmenu"&&l.settings.mpContext){return true}if(n.type==="mouseup"&&l.settings.mpMouse){return true}if(n.type==="click"&&l.settings.mpContext){return h.AltContextMenu(n,this)}var m=l.MSIE9events[n.type];return h[m].call(this,n)},getJaxFromMath:function(m){m=m.parentNode;do{m=m.nextSibling}while(m&&m.nodeName.toLowerCase()!=="script");return c.getJaxFor(m)},getHoverSpan:function(m,n){return n.firstChild},getHoverBBox:function(m,n,o){return h.getBBox(n.parentNode)},Zoom:function(n,u,s,m,r){n.root.toNativeMML(u);if(this.msieIE8HeightBug){u.style.position="absolute"}if(l.widthBug){u.style.width=u.parentNode.style.width=""}if(u.parentNode.style.width.match(/%$/)){u.parentNode.style.minWidth=Math.ceil(3*r/4)+"px"}var p=s.offsetWidth||s.scrollWidth,v=s.offsetHeight||s.scrollHeight;var t=u.offsetWidth,q=u.offsetHeight;if(l.widthBug||u.style.width.match(/%/)){var o=u.firstChild.firstChild.scrollWidth;if(o>t){t=o;u.parentNode.style.width=u.style.minWidth=t+"px"}}if(this.msieIE8HeightBug){u.style.position=""}return{Y:-h.getBBox(u.parentNode).h,mW:p,mH:v,zW:t,zH:q}},NAMEDSPACE:{negativeveryverythinmathspace:"-.0556em",negativeverythinmathspace:"-.1111em",negativethinmathspace:"-.1667em",negativemediummathspace:"-.2222em",negativethickmathspace:"-.2778em",negativeverythickmathspace:"-.3333em",negativeveryverythickmathspace:"-.3889em",veryverythinmathspace:".0556em",verythinmathspace:".1111em",thinmathspace:".1667em",mediummathspace:".2222em",thickmathspace:".2778em",verythickmathspace:".3333em",veryverythickmathspace:".3889em"}});c.Register.StartupHook("mml Jax Ready",function(){f=MathJax.ElementJax.mml;f.mbase.Augment({toNativeMML:function(r){var p=this.NativeMMLelement(this.type);this.NativeMMLattributes(p);for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}else{p.appendChild(this.NativeMMLelement("mrow"))}}r.appendChild(p)},NativeMMLattributes:function(w){var r=(this.type==="mstyle"?f.math.prototype.defaults:this.defaults);var t=(this.attrNames||f.copyAttributeNames),v=f.skipAttributes,o=f.copyAttributes;if(!this.attrNames){for(var p in r){if(!v[p]&&!o[p]&&r.hasOwnProperty(p)){if(this[p]!=null&&this[p]!==r[p]){w.setAttribute(p,this.NativeMMLattribute(this[p]))}}}}for(var s=0,q=t.length;s<q;s++){if(o[t[s]]===1&&!r.hasOwnProperty(t[s])){continue}var u=(this.attr||{})[t[s]];if(u==null){u=this[t[s]]}if(u!=null){w.setAttribute(t[s],this.NativeMMLattribute(u))}}this.NativeMMLclass(w)},NativeMMLclass:function(o){var q=[];if(this["class"]){q.push(this["class"])}if(this.isa(f.TeXAtom)){var p=["ORD","OP","BIN","REL","OPEN","CLOSE","PUNCT","INNER","VCENTER"][this.texClass];if(p){q.push("MJX-TeXAtom-"+p)}}if(this.mathvariant&&this.NativeMMLvariants[this.mathvariant]){q.push("MJX"+this.mathvariant)}if(this.variantForm){q.push("MJX-variant")}if(q.length){o.setAttribute("class",q.join(" "))}},NativeMMLattribute:function(o){o=String(o);if(l.NAMEDSPACE[o]){o=l.NAMEDSPACE[o]}else{if(o.match(/^\s*(([-+])?(\d+(\.\d*)?|\.\d+))\s*mu\s*$/)){o=(RegExp.$2||"")+((1/18)*RegExp.$3).toFixed(3).replace(/\.?0+$/,"")+"em"}else{if(this.NativeMMLvariants[o]){o=this.NativeMMLvariants[o]}}}return o},NativeMMLvariants:{"-tex-caligraphic":f.VARIANT.SCRIPT,"-tex-caligraphic-bold":f.VARIANT.BOLDSCRIPT,"-tex-oldstyle":f.VARIANT.NORMAL,"-tex-oldstyle-bold":f.VARIANT.BOLD,"-tex-mathit":f.VARIANT.ITALIC},NativeMMLelement:function(o){var p=(document.createElementNS?document.createElementNS(l.MMLnamespace,o):(c.Browser.mpNamespace?document.createElement("m:"+o):document.createElement(o)));p.isMathJax=true;return p}});f.mrow.Augment({toNativeMML:function(s){var r,p;if(this.inferred&&this.parent.inferRow){for(r=0,p=this.data.length;r<p;r++){if(this.data[r]){this.data[r].toNativeMML(s)}else{s.appendChild(this.NativeMMLelement("mrow"))}}}else{if(l.stretchyMoBug&&(this.open||this.close)){var q=this.NativeMMLelement("mfenced");this.NativeMMLattributes(q);r=0,p=this.data.length;if(this.open){q.setAttribute("open",this.open);r++}if(this.close){q.setAttribute("close",this.close);p--}var o=q;if(p-r+1>1){o=this.NativeMMLelement("mrow");s.appendChild(q);s=q}for(;r<p;r++){if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}s.appendChild(o)}else{this.SUPER(arguments).toNativeMML.call(this,s)}}}});f.msubsup.Augment({toNativeMML:function(s){var r=this.type;if(this.data[this.sup]==null){r="msub"}if(this.data[this.sub]==null){r="msup"}var p=this.NativeMMLelement(r);this.NativeMMLattributes(p);if(this.data[0]){delete this.data[0].inferred}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}}s.appendChild(p)}});f.munderover.Augment({toNativeMML:function(s){var r=this.type;if(this.data[this.under]==null){r="mover"}if(this.data[this.over]==null){r="munder"}var p=this.NativeMMLelement(r);this.NativeMMLattributes(p);if(this.data[0]){delete this.data[0].inferred}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}}s.appendChild(p)}});if(!i){var m=c.SplitList;f.mtable.Augment({toNativeMML:function(z){var s,q;if(l.tableSpacingBug){var A=this.getValues("rowspacing","columnspacing");this.nMMLtopPadding=m("0px "+A.rowspacing);this.nMMLleftPadding=m("0px "+A.columnspacing);var y=this.nMMLtopPadding,v=y.length;for(s=0,q=this.data.length;s<q;s++){if(this.data[s]){this.data[s].nMMLtopPadding=y[s<v?s:v-1]}}}if(l.tableLabelBug){for(s=0,q=this.data.length;s<q;s++){if(this.data[s]&&this.data[s].isa(f.mlabeledtr)){var u=c.config.displayAlign.charAt(0),w=this.Get("side").charAt(0);this.nMMLhasLabels=true;this.nMMLlaMatch=(u===w);this.nMMLforceWidth=(u==="c"||!!((this.width||"").match("%")));break}}}if(this.width&&this.ffTableWidthBug){var B=(this.style||"").replace(/;\s*$/,"").split(";");if(B[0]===""){B.shift()}B.push("width:"+this.width);this.style=B.join(";")}this.SUPER(arguments).toNativeMML.call(this,z);if(this.nMMLhasLabels){var r=z.firstChild;if(this.nMMLforceWidth||w!=="r"){var p=(u!=="l"?1:0)+(w==="l"?1:0);if(p){var t={columnalign:"left",columnwidth:"auto",columnspacing:"0px",columnlines:"none"};for(var o in t){if(t.hasOwnProperty(o)&&this[o]){var x=[t[o],t[o]].slice(2-p).join(" ")+" ";r.setAttribute(o,x+r.getAttribute(o))}}}}if(this.nMMLforceWidth||!this.nMMLlaMatch){r.setAttribute("width","100%")}}}});f.mtr.Augment({toNativeMML:function(v){this.SUPER(arguments).toNativeMML.call(this,v);var p=v.lastChild;if(l.tableSpacingBug){var r=this.parent.nMMLleftPadding,t=r.length;for(var w=p.firstChild,q=0;w;w=w.nextSibling,q++){a(w,this.nMMLtopPadding,r[q<t?q:t-1])}}if(l.tableLabelBug){var o=this.parent.nMMLforceWidth,u=this.parent.Get("side").charAt(0),s=c.config.displayAlign.charAt(0);if(this.parent.nMMLhasLabels&&p.firstChild){if(o||u!=="r"){j("Left",p.firstChild);if(s!=="l"){p.insertBefore(this.NativeMMLelement("mtd"),p.firstChild).setAttribute("style","padding:0")}if(u==="l"){p.insertBefore(this.NativeMMLelement("mtd"),p.firstChild).setAttribute("style","padding:0")}}if(o||u!=="l"){j("Right",p.lastChild)}}}}});f.mlabeledtr.Augment({toNativeMML:function(C){var t=this.NativeMMLelement("mtr");this.NativeMMLattributes(t);for(var u=1,s=this.data.length;u<s;u++){if(this.data[u]){this.data[u].toNativeMML(t)}else{t.appendChild(this.NativeMMLelement("mtd"))}}if(l.tableSpacingBug){var v=this.parent.nMMLleftPadding,y=v.length;u=0;for(var D=t.firstChild;D;D=D.nextSibling,u++){a(D,this.nMMLtopPadding,v[u<y?u:y-1])}}if(l.tableLabelBug&&this.data[0]){var z=this.parent.Get("side").charAt(0),x=c.config.displayAlign.charAt(0),q=c.config.displayIndent;this.data[0].toNativeMML(t);var A=t.lastChild,r=A;if(z===x){A.setAttribute("style","width:"+q);A.setAttribute("columnalign",c.config.displayAlign)}else{r=this.NativeMMLelement("mpadded");r.setAttribute("style","width:0");r.setAttribute("width","0px");r.appendChild(A.firstChild);A.appendChild(r)}j("",A);t.removeChild(A);var o=100,p=this.parent.nMMLforceWidth;if((this.parent.width||"").match(/%/)){o-=parseFloat(this.parent.width)}var B=o;if(p||z!=="r"){j("Left",t.firstChild);if(x!=="l"){if(x==="c"){B/=2}o-=B;t.insertBefore(this.NativeMMLelement("mtd"),t.firstChild).setAttribute("style","padding:0;width:"+B+"%")}if(z==="l"){t.insertBefore(A,t.firstChild)}}if(p||z!=="l"){j("Right",t.lastChild);if(x!=="r"){t.appendChild(this.NativeMMLelement("mtd")).setAttribute("style","padding:0;width:"+o+"%")}if(z==="r"){if(z!==x){r.setAttribute("lspace","-1width")}t.appendChild(A)}}}C.appendChild(t)}});f.mtd.Augment({toNativeMML:function(r){var p=r.appendChild(this.NativeMMLelement(this.type));this.NativeMMLattributes(p);if(l.mtdWidthBug){l.adjustWidths.push(p);p=p.appendChild(this.NativeMMLelement("mrow"))}for(var q=0,o=this.data.length;q<o;q++){if(this.data[q]){this.data[q].toNativeMML(p)}else{p.appendChild(this.NativeMMLelement("mrow"))}}}});f.mspace.Augment({toNativeMML:function(q){this.SUPER(arguments).toNativeMML.call(this,q);if(l.spaceWidthBug&&this.width){var r=q.lastChild;var p=r.getAttribute("width");var o=(r.getAttribute("style")||"").replace(/;?\s*/,"; ");r.setAttribute("style",o+"width:"+p)}}});var n=g.fileURL(MathJax.OutputJax.fontDir+"/HTML-CSS/TeX/otf");l.Augment({config:{styles:{'[class="MJX-tex-oldstyle"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-oldstyle-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},'[class="MJX-tex-caligraphic"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB"},'[class="MJX-tex-caligraphic-bold"]':{"font-family":"MathJax_Caligraphic, MathJax_Caligraphic-WEB","font-weight":"bold"},"@font-face /*1*/":{"font-family":"MathJax_Caligraphic-WEB",src:"url('"+n+"/MathJax_Caligraphic-Regular.otf')"},"@font-face /*2*/":{"font-family":"MathJax_Caligraphic-WEB","font-weight":"bold",src:"url('"+n+"/MathJax_Caligraphic-Bold.otf')"}}}});if(!this.handlesVariants){l.Augment({config:{styles:{'[mathvariant="double-struck"]':{"font-family":"MathJax_AMS, 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t=((this.data[0]||{data:[]}).data[0]||{});if(t.nMMLhasLabels){if(t.nMMLforceWidth||!t.nMMLlaMatch){A.setAttribute("style","width:100%");if(u){A.parentNode.setAttribute("style","width:100%")}}if(t.nMMLlaMatch){if(y.parentNode.parentNode.nodeName.toLowerCase()==="div"){y.parentNode.parentNode.style.setProperty("margin-"+c.config.displayAlign,"0px","important")}}}var x=l.isFullWidth(w);if(x){y.style.width=y.parentNode.style.width="100%"}y.appendChild(w);if(l.widthBug&&!x){y.style.width=(w.firstChild.scrollWidth/l.ex/l.scale).toFixed(3)+"ex";if(p){p.NativeMML.scrollWidth=w.firstChild.scrollWidth}}if(l.adjustWidths.length){var z=[];for(v=0,r=l.adjustWidths.length;v<r;v++){A=l.adjustWidths[v];var o=A.getAttribute("style")||"";if(!o.match(/(^|;)\s*min-width:/)){var q=A.firstChild.scrollWidth;z.push(q);q=(q/l.ex).toFixed(3)+"ex";o=o.replace(/;?\s*$/,"; 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o=this.NativeMMLelement(t?this.type:"mrow");this.NativeMMLattributes(o);o.removeAttribute("separators");if(t){o.setAttribute("open",q.open);o.setAttribute("close",q.close);if(this.data.length>1){w.appendChild(o);w=o;o=this.NativeMMLelement("mrow")}}else{o.removeAttribute("open");o.removeAttribute("close")}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.open;o.appendChild(r)}for(u=0,p=this.data.length;u<p;u++){if(q.separators&&u>0){r=this.NativeMMLelement("mo");r.setAttribute("separator","true");r.textContent=q.separators[u-1];o.appendChild(r)}if(this.data[u]){this.data[u].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}}if(!t){r=this.NativeMMLelement("mo");r.setAttribute("fence","true");r.textContent=q.close;o.appendChild(r)}w.appendChild(o)}});f.TeXAtom.Augment({toNativeMML:function(p){var o=this.NativeMMLelement("mrow");this.NativeMMLattributes(o);this.data[0].toNativeMML(o);p.appendChild(o)}});f.chars.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.entity.Augment({toNativeMML:function(o){o.appendChild(document.createTextNode(this.toString()))}});f.xml.Augment({toNativeMML:function(q){for(var p=0,o=this.data.length;p<o;p++){q.appendChild(this.data[p].cloneNode(true))}}});f.mi.Augment({toNativeMML:function(p){this.SUPER(arguments).toNativeMML.call(this,p);if(l.miItalicBug){if(this.Get("mathvariant")===f.VARIANT.NORMAL){var o=p.lastChild;o.setAttribute("mathvariant",f.VARIANT.NORMAL)}}}});f.mo.Augment({toNativeMML:function(t){this.SUPER(arguments).toNativeMML.call(this,t);if(l.webkitMoSpacingBug){var o=0,s=0,v=this.parent;if(v&&v.type==="mrow"&&(v.inferred||!v.isEmbellished())){var q=this.getValues("lspace","rspace");o=q.lspace,s=q.rspace;if(l.NAMEDSPACE[o]){o=l.NAMEDSPACE[o]}if(l.NAMEDSPACE[s]){s=l.NAMEDSPACE[s]}}var u=t.lastChild;var r=e.Element("span");r.style.cssText=(u.getAttribute("style")||"");r.style.setProperty("-webkit-margin-start",o);r.style.setProperty("-webkit-margin-end",s);u.setAttribute("style",r.style.cssText)}}});f.mmultiscripts.Augment({toNativeMML:function(s){if(!l.mmultiscriptsBug||this.data.length===0){this.SUPER(arguments).toNativeMML.call(this,s);return}var q=this.NativeMMLelement("mrow");this.NativeMMLattributes(q);if(this.data[0]){this.data[0].toNativeMML(q)}else{q.appendChild(this.NativeMMLelement("mrow"))}var t=q.removeChild(q.lastChild);var p=this.data.length,r,o;for(r=1;r<p;r+=2){if(this.data[r].type==="mprescripts"){break}o=this.NativeMMLelement("msubsup");o.appendChild(t);if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}if(r+1<p&&this.data[r+1]){this.data[r+1].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}t=o}q.appendChild(t);for(r++;r<p;r+=2){o=this.NativeMMLelement("msubsup");o.appendChild(this.NativeMMLelement("mrow"));if(this.data[r]){this.data[r].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}if(r+1<p&&this.data[r+1]){this.data[r+1].toNativeMML(o)}else{o.appendChild(this.NativeMMLelement("mrow"))}q.insertBefore(o,t)}s.appendChild(q)}});c.Register.StartupHook("TeX mathchoice Ready",function(){f.TeXmathchoice.Augment({toNativeMML:function(o){this.Core().toNativeMML(o)}})});setTimeout(MathJax.Callback(["loadComplete",l,"jax.js"]),0)});c.Browser.Select({MSIE:function(m){var n=(document.documentMode||0);l.msieIE8HeightBug=(n===8)},Opera:function(m){l.operaPositionBug=true;l.stretchyMoBug=true;l.tableLabelBug=true;l.mfencedBug=true;l.miBug=true;l.mmultiscriptsBug=true},Firefox:function(m){var n=m.versionAtLeast("29.0");l.ffTableWidthBug=!m.versionAtLeast("13.0");l.forceReflow=!n;l.widthBug=!n;l.mtdWidthBug=true;l.handlesVariants=n;l.spaceWidthBug=!m.versionAtLeast("20.0");l.tableSpacingBug=!m.versionAtLeast("33.0");l.tableLabelBug=true;l.mfencedBug=true},Chrome:function(m){l.tableSpacingBug=true;l.tableLabelBug=true;l.mfencedBug=true},Safari:function(m){l.tableSpacingBug=true;l.tableLabelBug=true;l.mfencedBug=true;l.miItalicBug=true;l.webkitMoSpacingBug=true;l.spaceWidthBug=true;l.mmultiscriptsBug=true}});c.Register.StartupHook("End Cookie",function(){if(c.config.menuSettings.zoom!=="None"){g.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.OutputJax.NativeMML,MathJax.Hub,MathJax.Ajax,MathJax.HTML);
    20.