diff options
author | maheshgudi | 2017-12-13 17:28:26 +0530 |
---|---|---|
committer | maheshgudi | 2017-12-13 17:28:26 +0530 |
commit | 3ddd28edaea9174c89a81cc7938f95ce12610fdf (patch) | |
tree | ddab15e2256247bc2d9ff111a6802ddc70c967d0 /yaksh/static | |
parent | 63326f9519478f0d9bfb0b843e5dac8ab29428f4 (diff) | |
download | online_test-3ddd28edaea9174c89a81cc7938f95ce12610fdf.tar.gz online_test-3ddd28edaea9174c89a81cc7938f95ce12610fdf.tar.bz2 online_test-3ddd28edaea9174c89a81cc7938f95ce12610fdf.zip |
Add Mathjax to the repo
Diffstat (limited to 'yaksh/static')
26 files changed, 126 insertions, 0 deletions
diff --git a/yaksh/static/yaksh/js/mathjax/MathJax.js b/yaksh/static/yaksh/js/mathjax/MathJax.js new file mode 100644 index 0000000..792f7e4 --- /dev/null +++ b/yaksh/static/yaksh/js/mathjax/MathJax.js @@ -0,0 +1,19 @@ +/* + * /MathJax.js + * + * Copyright (c) 2009-2017 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +if(document.getElementById&&document.childNodes&&document.createElement){if(!(window.MathJax&&MathJax.Hub)){if(window.MathJax){window.MathJax={AuthorConfig:window.MathJax}}else{window.MathJax={}}MathJax.isPacked=true;MathJax.version="2.7.2";MathJax.fileversion="2.7.2";MathJax.cdnVersion="2.7.2";MathJax.cdnFileVersions={};(function(d){var b=window[d];if(!b){b=window[d]={}}var e=[];var c=function(f){var g=f.constructor;if(!g){g=function(){}}for(var h in f){if(h!=="constructor"&&f.hasOwnProperty(h)){g[h]=f[h]}}return g};var a=function(){return function(){return arguments.callee.Init.call(this,arguments)}};b.Object=c({constructor:a(),Subclass:function(f,h){var g=a();g.SUPER=this;g.Init=this.Init;g.Subclass=this.Subclass;g.Augment=this.Augment;g.protoFunction=this.protoFunction;g.can=this.can;g.has=this.has;g.isa=this.isa;g.prototype=new this(e);g.prototype.constructor=g;g.Augment(f,h);return g},Init:function(f){var g=this;if(f.length===1&&f[0]===e){return g}if(!(g instanceof f.callee)){g=new f.callee(e)}return g.Init.apply(g,f)||g},Augment:function(f,g){var h;if(f!=null){for(h in f){if(f.hasOwnProperty(h)){this.protoFunction(h,f[h])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){this.protoFunction("toString",f.toString)}}if(g!=null){for(h in g){if(g.hasOwnProperty(h)){this[h]=g[h]}}}return this},protoFunction:function(g,f){this.prototype[g]=f;if(typeof f==="function"){f.SUPER=this.SUPER.prototype}},prototype:{Init:function(){},SUPER:function(f){return f.callee.SUPER},can:function(f){return typeof(this[f])==="function"},has:function(f){return typeof(this[f])!=="undefined"},isa:function(f){return(f instanceof Object)&&(this instanceof f)}},can:function(f){return this.prototype.can.call(this,f)},has:function(f){return this.prototype.has.call(this,f)},isa:function(g){var f=this;while(f){if(f===g){return true}else{f=f.SUPER}}return false},SimpleSUPER:c({constructor:function(f){return this.SimpleSUPER.define(f)},define:function(f){var h={};if(f!=null){for(var g in f){if(f.hasOwnProperty(g)){h[g]=this.wrap(g,f[g])}}if(f.toString!==this.prototype.toString&&f.toString!=={}.toString){h.toString=this.wrap("toString",f.toString)}}return h},wrap:function(i,h){if(typeof(h)!=="function"||!h.toString().match(/\.\s*SUPER\s*\(/)){return h}var g=function(){this.SUPER=g.SUPER[i];try{var f=h.apply(this,arguments)}catch(j){delete this.SUPER;throw j}delete this.SUPER;return f};g.toString=function(){return h.toString.apply(h,arguments)};return g}})});b.Object.isArray=Array.isArray||function(f){return Object.prototype.toString.call(f)==="[object Array]"};b.Object.Array=Array})("MathJax");(function(BASENAME){var BASE=window[BASENAME];if(!BASE){BASE=window[BASENAME]={}}var isArray=BASE.Object.isArray;var CALLBACK=function(data){var cb=function(){return arguments.callee.execute.apply(arguments.callee,arguments)};for(var id in 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s=h.Element("span",{isMathJax:true,id:q.hover.id+"Menu",className:"MathJax_Menu_Button",style:{display:"inline-block","z-index":1,width:0,height:0,position:"relative"}},[["span",{className:"MathJax_Hover_Arrow",isMathJax:true,math:u,onclick:this.HoverMenu,jax:t.id,style:{left:this.Px(y.w+A+x+(y.x||0)+o.button.x),top:this.Px(-y.h-z-x-(y.y||0)-o.button.y),opacity:0,filter:"alpha(opacity=0)"}},[["span",{isMathJax:true},"\u25BC"]]]]);if(y.width){r.style.width=s.style.width=y.width;r.style.marginRight=s.style.marginRight="-"+y.width;r.firstChild.style.width=y.width;s.firstChild.style.left="";s.firstChild.style.right=this.Px(o.button.wx)}v.parentNode.insertBefore(r,v);if(w){v.parentNode.insertBefore(s,v)}if(v.style){v.style.position="relative"}this.ReHover(q)},ReHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}q.hover.remove=setTimeout(g(["UnHover",this,q]),o.fadeoutDelay);this.HoverFadeTimer(q,o.fadeinInc)},UnHover:function(q){if(!q.hover.nofade){this.HoverFadeTimer(q,-o.fadeoutInc,o.fadeoutStart)}},HoverFade:function(q){delete q.hover.timer;q.hover.opacity=Math.max(0,Math.min(1,q.hover.opacity+q.hover.inc));q.hover.opacity=Math.floor(1000*q.hover.opacity)/1000;var s=document.getElementById(q.hover.id),r=document.getElementById(q.hover.id+"Menu");s.firstChild.style.opacity=q.hover.opacity;s.firstChild.style.filter="alpha(opacity="+Math.floor(100*q.hover.opacity)+")";if(r){r.firstChild.style.opacity=q.hover.opacity;r.firstChild.style.filter=s.style.filter}if(q.hover.opacity===1){return}if(q.hover.opacity>0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return 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r=q.versionAtLeast("8.0");c.msieBorderWidthBug=(document.compatMode==="BackCompat");c.msieEventBug=q.isIE9;c.msieAlignBug=(!r||s<8);if(s<9){n.LEFTBUTTON=1}},Safari:function(q){c.safariContextMenuBug=true},Opera:function(q){c.operaPositionBug=true},Konqueror:function(q){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=o=d.CombineConfig("MathEvents",o);var e=function(){var q=o.styles[".MathJax_Hover_Frame"];q.border=o.frame.bwidth+"px solid "+o.frame.bcolor+" ! important";q["box-shadow"]=q["-webkit-box-shadow"]=q["-moz-box-shadow"]=q["-khtml-box-shadow"]="0px 0px "+o.frame.hwidth+" "+o.frame.hcolor};g.Queue(d.Register.StartupHook("End Config",{}),[e],["getImages",f],["Styles",l,o.styles],["Post",d.Startup.signal,"MathEvents 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true}if(!h[l]){return true}return h[l](n,m)},Click:function(m,l){if(this.settings.zoom==="Click"){return this.Zoom(m,l)}},DblClick:function(m,l){if(this.settings.zoom==="Double-Click"||this.settings.zoom==="DoubleClick"){return this.Zoom(m,l)}},Hover:function(m,l){if(this.settings.zoom==="Hover"){this.Zoom(m,l);return true}return false},Zoom:function(o,u){this.Remove();b.ClearHoverTimer();g.ClearSelection();var s=MathJax.OutputJax[u.jaxID];var p=s.getJaxFromMath(u);if(p.hover){b.UnHover(p)}var q=this.findContainer(u);var l=Math.floor(0.85*q.clientWidth),t=Math.max(document.body.clientHeight,document.documentElement.clientHeight);if(this.getOverflow(q)!=="visible"){t=Math.min(q.clientHeight,t)}t=Math.floor(0.85*t);var n=d.Element("span",{id:"MathJax_ZoomFrame"},[["span",{id:"MathJax_ZoomOverlay",onmousedown:this.Remove}],["span",{id:"MathJax_Zoom",onclick:this.Remove,style:{visibility:"hidden",fontSize:this.settings.zscale}},[["span",{style:{display:"inline-block","white-space":"nowrap"}}]]]]);var z=n.lastChild,w=z.firstChild,r=n.firstChild;u.parentNode.insertBefore(n,u);u.parentNode.insertBefore(u,n);if(w.addEventListener){w.addEventListener("mousedown",this.Remove,true)}var m=z.offsetWidth||z.clientWidth;l-=m;t-=m;z.style.maxWidth=l+"px";z.style.maxHeight=t+"px";if(this.msieTrapEventBug){var y=d.Element("span",{id:"MathJax_ZoomEventTrap",onmousedown:this.Remove});n.insertBefore(y,z)}if(this.msieZIndexBug){var v=d.addElement(document.body,"img",{src:"about:blank",id:"MathJax_ZoomTracker",width:0,height:0,style:{width:0,height:0,position:"relative"}});n.style.position="relative";n.style.zIndex=i.styles["#MathJax_ZoomOverlay"]["z-index"];n=v}var x=s.Zoom(p,w,u,l,t);if(this.msiePositionBug){if(this.msieSizeBug){z.style.height=x.zH+"px";z.style.width=x.zW+"px"}if(z.offsetHeight>t){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m<l&&z.offsetHeight-m<t){z.style.overflow="visible"}this.Position(z,x);if(this.msieTrapEventBug){y.style.height=z.clientHeight+"px";y.style.width=z.clientWidth+"px";y.style.left=(parseFloat(z.style.left)+z.clientLeft)+"px";y.style.top=(parseFloat(z.style.top)+z.clientTop)+"px"}z.style.visibility="";if(this.settings.zoom==="Hover"){r.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",p]);return e(o)},Position:function(p,r){p.style.display="none";var q=this.Resize(),m=q.x,s=q.y,l=r.mW;p.style.display="";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 q=document.getElementById("MathJax_ZoomFrame"),l=document.getElementById("MathJax_ZoomOverlay");var o=h.getXY(q),n=h.findContainer(q);if(h.getOverflow(n)!=="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");if(!l){return}l.style.display="none";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";l.style.display=""},findContainer:function(l){l=l.parentNode;while(l.parentNode&&l!==document.body&&h.getOverflow(l)==="visible"){l=l.parentNode}return l},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); +(function(f,o,q,e,r){var p="2.7.2";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 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#808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 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6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var 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e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o<n;o++){p=arguments[o];if(!p){continue}if(p instanceof i.mbase){p=b.mml(p)}p.global=this.global;q=(this.data.length?this.Top().checkItem(p):true);if(q instanceof Array){this.Pop();this.Push.apply(this,q)}else{if(q instanceof b){this.Pop();this.Push(q)}else{if(q){this.data.push(p);if(p.env){if(p.copyEnv!==false){for(var r in this.env){if(this.env.hasOwnProperty(r)){p.env[r]=this.env[r]}}}this.env=p.env}else{p.env=this.env}}}}}},Pop:function(){var m=this.data.pop();if(!m.isOpen){delete m.env}this.env=(this.data.length?this.Top().env:{});return m},Top:function(m){if(m==null){m=1}if(this.data.length<m){return null}return this.data[this.data.length-m]},Prev:function(m){var n=this.Top();if(m){return n.data[n.data.length-1]}else{return n.Pop()}},toString:function(){return"stack[\n 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false},With:function(m){for(var n in m){if(m.hasOwnProperty(n)){this[n]=m[n]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(m){this.SUPER(arguments).Init.call(this);this.global=m},checkItem:function(m){if(m.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,m)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(n){if(n.type==="close"){var m=this.mmlData();return b.mml(i.TeXAtom(m))}return this.SUPER(arguments).checkItem.call(this,n)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(m){if(this.data[0].type!=="msubsup"){return[i.msup(this.data[0],this.data[1]),m]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],m]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSub","Missing open brace for subscript"],checkItem:function(m){if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{m.data[0]=i.mrow(this.primes.With({variantForm:true}),m.data[0])}}this.data[0].SetData(this.position,m.data[0]);if(this.movesupsub!=null){this.data[0].movesupsub=this.movesupsub}return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,m)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(o,m){if(o.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",o.name])}if(o.isClose){var n=i.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){n.linethickness=this.thickness}if(this.open||this.close){n.texWithDelims=true;n=d.fixedFence(this.open,n,this.close)}return[b.mml(n),o]}return this.SUPER(arguments).checkItem.call(this,o)},toString:function(){return"over["+this.num+" / "+this.data.join("; ")+"]"}});b.left=b.Subclass({type:"left",isOpen:true,delim:"(",stopError:["ExtraLeftMissingRight","Extra \\left or missing \\right"],checkItem:function(m){if(m.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),m.delim))}return this.SUPER(arguments).checkItem.call(this,m)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(m){if(m.type==="end"){if(m.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,m.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(m.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,m)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(n){if(!n.isClose){return this.SUPER(arguments).checkItem.call(this,n)}var m=i.mstyle.apply(i,this.data).With(this.styles);return[b.mml(m),n]}});b.position=b.Subclass({type:"position",checkItem:function(n){if(n.isClose){d.Error(["MissingBoxFor","Missing box for %1",this.name])}if(n.isNotStack){var m=n.mmlData();switch(this.move){case"vertical":m=i.mpadded(m).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(m)];case"horizontal":return[b.mml(this.left),n,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,n)}});b.array=b.Subclass({type:"array",isOpen:true,copyEnv:false,arraydef:{},Init:function(){this.table=[];this.row=[];this.frame=[];this.hfill=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(n){if(n.isClose&&n.type!=="over"){if(n.isEntry){this.EndEntry();this.clearEnv();return false}if(n.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var o=this.arraydef.scriptlevel;delete this.arraydef.scriptlevel;var m=i.mtable.apply(i,this.table).With(this.arraydef);if(this.frame.length===4){m.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){m.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( 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n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(m){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(o){var n,m;if(this.stack.env.font){n={mathvariant:this.stack.env.font}}if(g.remap[o]){o=g.remap[o];if(f(o)){n=o[1];o=o[0]}m=i.mo(i.entity("#x"+o)).With(n)}else{m=i.mo(o).With(n)}if(m.autoDefault("stretchy",true)){m.stretchy=false}if(m.autoDefault("texClass",true)==""){m=i.TeXAtom(m)}this.Push(this.mmlToken(m))},SetFont:function(n,m){this.stack.env.font=m},SetStyle:function(n,m,o,p){this.stack.env.style=m;this.stack.env.level=p;this.Push(b.style().With({styles:{displaystyle:o,scriptlevel:p}}))},SetSize:function(m,n){this.stack.env.size=n;this.Push(b.style().With({styles:{mathsize:n+"em"}}))},Color:function(o){var n=this.GetArgument(o);var m=this.stack.env.color;this.stack.env.color=n;var p=this.ParseArg(o);if(m){this.stack.env.color}else{delete this.stack.env.color}this.Push(i.mstyle(p).With({mathcolor:n}))},Spacer:function(m,n){this.Push(i.mspace().With({width:n,mathsize:i.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(m){this.Push(b[m.substr(1)]().With({delim:this.GetDelimiter(m)}))},Middle:function(m){var n=this.GetDelimiter(m);this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.CLOSE}));if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",m])}this.Push(i.mo(n).With({stretchy:true}));this.Push(i.TeXAtom().With({texClass:i.TEXCLASS.OPEN}))},NamedFn:function(n,o){if(!o){o=n.substr(1)}var m=i.mi(o).With({texClass:i.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(m)))},NamedOp:function(n,o){if(!o){o=n.substr(1)}o=o.replace(/ /,"\u2006");var m=i.mo(o).With({movablelimits:true,movesupsub:true,form:i.FORM.PREFIX,texClass:i.TEXCLASS.OP});m.useMMLspacing&=~m.SPACE_ATTR.form;this.Push(this.mmlToken(m))},Limits:function(n,m){var p=this.stack.Prev("nopop");if(!p||(p.Get("texClass")!==i.TEXCLASS.OP&&p.movesupsub==null)){d.Error(["MisplacedLimits","%1 is allowed only on operators",n])}var o=this.stack.Top();if(p.type==="munderover"&&!m){p=o.data[o.data.length-1]=i.msubsup.apply(i.subsup,p.data)}else{if(p.type==="msubsup"&&m){p=o.data[o.data.length-1]=i.munderover.apply(i.underover,p.data)}}p.movesupsub=(m?true:false);p.Core().movablelimits=false;if(p.movablelimits){p.movablelimits=false}},Over:function(o,n,p){var m=b.over().With({name:o});if(n||p){m.open=n;m.close=p}else{if(o.match(/withdelims$/)){m.open=this.GetDelimiter(o);m.close=this.GetDelimiter(o)}}if(o.match(/^\\above/)){m.thickness=this.GetDimen(o)}else{if(o.match(/^\\atop/)||n||p){m.thickness=0}}this.Push(m)},Frac:function(n){var m=this.ParseArg(n);var o=this.ParseArg(n);this.Push(i.mfrac(m,o))},Sqrt:function(p){var q=this.GetBrackets(p),m=this.GetArgument(p);if(m==="\\frac"){m+="{"+this.GetArgument(m)+"}{"+this.GetArgument(m)+"}"}var o=d.Parse(m,this.stack.env).mml();if(!q){o=i.msqrt.apply(i,o.array())}else{o=i.mroot(o,this.parseRoot(q))}this.Push(o)},Root:function(o){var p=this.GetUpTo(o,"\\of");var m=this.ParseArg(o);this.Push(i.mroot(m,this.parseRoot(p)))},parseRoot:function(r){var o=this.stack.env,m=o.inRoot;o.inRoot=true;var q=d.Parse(r,o);r=q.mml();var p=q.stack.global;if(p.leftRoot||p.upRoot){r=i.mpadded(r);if(p.leftRoot){r.width=p.leftRoot}if(p.upRoot){r.voffset=p.upRoot;r.height=p.upRoot}}o.inRoot=m;return r},MoveRoot:function(m,p){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",m])}if(this.stack.global[p]){d.Error(["MultipleMoveRoot","Multiple use of %1",m])}var o=this.GetArgument(m);if(!o.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",m])}o=(o/15)+"em";if(o.substr(0,1)!=="-"){o="+"+o}this.stack.global[p]=o},Accent:function(o,m,s){var r=this.ParseArg(o);var q={accent:true};if(this.stack.env.font){q.mathvariant=this.stack.env.font}var n=this.mmlToken(i.mo(i.entity("#x"+m)).With(q));n.stretchy=(s?true:false);var p=(r.isEmbellished()?r.CoreMO():r);if(p.isa(i.mo)){p.movablelimits=false}this.Push(i.TeXAtom(i.munderover(r,null,n).With({accent:true})))},UnderOver:function(o,s,m,q){var r={o:"over",u:"under"}[o.charAt(1)];var p=this.ParseArg(o);if(p.Get("movablelimits")){p.movablelimits=false}if(p.isa(i.munderover)&&p.isEmbellished()){p.Core().With({lspace:0,rspace:0});p=i.mrow(i.mo().With({rspace:0}),p)}var n=i.munderover(p,null,null);n.SetData(n[r],this.mmlToken(i.mo(i.entity("#x"+s)).With({stretchy:true,accent:!q})));if(m){n=i.TeXAtom(n).With({texClass:i.TEXCLASS.OP,movesupsub:true})}this.Push(n.With({subsupOK:true}))},Overset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);if(n.movablelimits){n.movablelimits=false}this.Push(i.mover(n,o))},Underset:function(m){var o=this.ParseArg(m),n=this.ParseArg(m);if(n.movablelimits){n.movablelimits=false}this.Push(i.munder(n,o))},TeXAtom:function(p,r){var q={texClass:r},o;if(r==i.TEXCLASS.OP){q.movesupsub=q.movablelimits=true;var m=this.GetArgument(p);var n=m.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(n){q.mathvariant=i.VARIANT.NORMAL;o=b.fn(this.mmlToken(i.mi(n[1]).With(q)))}else{o=b.fn(i.TeXAtom(d.Parse(m,this.stack.env).mml()).With(q))}}else{o=i.TeXAtom(this.ParseArg(p)).With(q)}this.Push(o)},MmlToken:function(o){var p=this.GetArgument(o),m=this.GetBrackets(o,"").replace(/^\s+/,""),s=this.GetArgument(o),r={attrNames:[]},n;if(!i[p]||!i[p].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",p])}while(m!==""){n=m.match(/^([a-z]+)\s*=\s*('[^']*'|"[^"]*"|[^ ,]*)\s*,?\s*/i);if(!n){d.Error(["InvalidMathMLAttr","Invalid MathML attribute: %1",m])}if(i[p].prototype.defaults[n[1]]==null&&!this.MmlTokenAllow[n[1]]){d.Error(["UnknownAttrForElement","%1 is not a recognized attribute for %2",n[1],p])}var q=this.MmlFilterAttribute(n[1],n[2].replace(/^(['"])(.*)\1$/,"$2"));if(q){if(q.toLowerCase()==="true"){q=true}else{if(q.toLowerCase()==="false"){q=false}}r[n[1]]=q;r.attrNames.push(n[1])}m=m.substr(n[0].length)}this.Push(this.mmlToken(i[p](s).With(r)))},MmlFilterAttribute:function(m,n){return n},MmlTokenAllow:{fontfamily:1,fontsize:1,fontweight:1,fontstyle:1,color:1,background:1,id:1,"class":1,href:1,style:1},Strut:function(m){this.Push(i.mpadded(i.mrow()).With({height:"8.6pt",depth:"3pt",width:0}))},Phantom:function(n,m,o){var p=i.mphantom(this.ParseArg(n));if(m||o){p=i.mpadded(p);if(o){p.height=p.depth=0}if(m){p.width=0}}this.Push(i.TeXAtom(p))},Smash:function(o){var n=this.trimSpaces(this.GetBrackets(o,""));var m=i.mpadded(this.ParseArg(o));switch(n){case"b":m.depth=0;break;case"t":m.height=0;break;default:m.height=m.depth=0}this.Push(i.TeXAtom(m))},Lap:function(n){var m=i.mpadded(this.ParseArg(n)).With({width:0});if(n==="\\llap"){m.lspace="-1width"}this.Push(i.TeXAtom(m))},RaiseLower:function(m){var n=this.GetDimen(m);var o=b.position().With({name:m,move:"vertical"});if(n.charAt(0)==="-"){n=n.slice(1);m={raise:"\\lower",lower:"\\raise"}[m.substr(1)]}if(m==="\\lower"){o.dh="-"+n;o.dd="+"+n}else{o.dh="+"+n;o.dd="-"+n}this.Push(o)},MoveLeftRight:function(m){var p=this.GetDimen(m);var o=(p.charAt(0)==="-"?p.slice(1):"-"+p);if(m==="\\moveleft"){var n=p;p=o;o=n}this.Push(b.position().With({name:m,move:"horizontal",left:i.mspace().With({width:p,mathsize:i.SIZE.NORMAL}),right:i.mspace().With({width:o,mathsize:i.SIZE.NORMAL})}))},Hskip:function(m){this.Push(i.mspace().With({width:this.GetDimen(m),mathsize:i.SIZE.NORMAL}))},Rule:function(n,p){var m=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var q={width:m,height:o,depth:r};if(p!=="blank"){q.mathbackground=(this.stack.env.color||"black")}this.Push(i.mspace().With(q))},rule:function(p){var n=this.GetBrackets(p),m=this.GetDimen(p),q=this.GetDimen(p);var o=i.mspace().With({width:m,height:q,mathbackground:(this.stack.env.color||"black")});if(n){o=i.mpadded(o).With({voffset:n});if(n.match(/^\-/)){o.height=n;o.depth="+"+n.substr(1)}else{o.height="+"+n}}this.Push(o)},MakeBig:function(m,p,n){n*=g.p_height;n=String(n).replace(/(\.\d\d\d).+/,"$1")+"em";var o=this.GetDelimiter(m,true);this.Push(i.TeXAtom(i.mo(o).With({minsize:n,maxsize:n,fence:true,stretchy:true,symmetric:true})).With({texClass:p}))},BuildRel:function(m){var n=this.ParseUpTo(m,"\\over");var o=this.ParseArg(m);this.Push(i.TeXAtom(i.munderover(o,null,n)).With({texClass:i.TEXCLASS.REL}))},HBox:function(m,n){this.Push.apply(this,this.InternalMath(this.GetArgument(m),n))},FBox:function(m){this.Push(i.menclose.apply(i,this.InternalMath(this.GetArgument(m))).With({notation:"box"}))},Not:function(m){this.Push(b.not())},Dots:function(m){this.Push(b.dots().With({ldots:this.mmlToken(i.mo(i.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(i.mo(i.entity("#x22EF")).With({stretchy:false}))}))},Require:function(m){var n=this.GetArgument(m).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,n)},Extension:function(m,n,o){if(m&&!typeof(m)==="string"){m=m.name}n=d.extensionDir+"/"+n;if(!n.match(/\.js$/)){n+=".js"}if(!j.loaded[j.fileURL(n)]){if(m!=null){delete g[o||"macros"][m.replace(/^\\/,"")]}c.RestartAfter(j.Require(n))}},Macro:function(o,r,q,s){if(q){var n=[];if(s!=null){var m=this.GetBrackets(o);n.push(m==null?s:m)}for(var p=n.length;p<q;p++){n.push(this.GetArgument(o))}r=this.SubstituteArgs(n,r)}this.string=this.AddArgs(r,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(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(q<n){var u=o.charAt(q);if(u==="{"){t++;q++}else{if(u==="}"){if(t===0){n=0}else{t--;if(t===0&&s<0){s=q-this.i}q++}}else{if(u==="&"&&t===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(u==="\\"){if(o.substr(q).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){n=0}else{q+=2}}else{q++}}}}}var r=o.substr(this.i,q-this.i);if(!r.match(/^\s*\\text[^a-zA-Z]/)||s!==r.replace(/\s+$/,"").length-1){this.Push.apply(this,this.InternalMath(r,0));this.i=q}}},Cr:function(m){this.Push(b.cell().With({isCR:true,name:m}))},CrLaTeX:function(m){var q;if(this.string.charAt(this.i)==="["){q=this.GetBrackets(m,"").replace(/ /g,"").replace(/,/,".");if(q&&!this.matchDimen(q)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",m])}}this.Push(b.cell().With({isCR:true,name:m,linebreak:true}));var p=this.stack.Top();if(p.isa(b.array)){if(q&&p.arraydef.rowspacing){var o=p.arraydef.rowspacing.split(/ 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n=o.MathJax.elementJax,r=n.root,p=document.getElementById(n.inputID+"-Frame"),t=(n.PHTML.display?p.parentNode:p);this.initPHTML(r,p);try{r.toPreviewHTML(p)}catch(q){if(q.restart){while(p.firstChild){p.removeChild(p.firstChild)}}throw q}t.className=t.className.split(/ /)[0];if(this.hideProcessedMath){t.className+=" MathJax_Processed";if(o.MathJax.preview){n.PHTML.preview=o.MathJax.preview;delete o.MathJax.preview}}},postTranslate:function(s){var o=s.jax[this.id];if(!this.hideProcessedMath){return}for(var q=0,n=o.length;q<n;q++){var p=o[q];if(p&&p.MathJax.elementJax){p.previousSibling.className=p.previousSibling.className.split(/ /)[0];var r=p.MathJax.elementJax.PHTML;if(r.preview){r.preview.innerHTML="";r.preview.style.display="none";p.MathJax.preview=r.preview;delete r.preview}}}},getJaxFromMath:function(n){if(n.parentNode.className.match(/MathJax_PHTML_Display/)){n=n.parentNode}do{n=n.nextSibling}while(n&&n.nodeName.toLowerCase()!=="script");return 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t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" 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t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return 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q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;p<n;p++){this.PHTMLaddChild(q,"sep"+p,{});this.PHTMLaddChild(q,p,{})}this.PHTMLaddChild(q,"close",{});var o=this.PHTML.h,r=this.PHTML.d;this.PHTMLstretchChild("open",o,r);for(p=0,n=this.data.length;p<n;p++){this.PHTMLstretchChild("sep"+p,o,r);this.PHTMLstretchChild(p,o,r)}this.PHTMLstretchChild("close",o,r);return q}});h.mrow.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var p=this.PHTML.h,r=this.PHTML.d;for(var o=0,n=this.data.length;o<n;o++){this.PHTMLstretchChild(o,p,r)}return q}});h.mstyle.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);this.PHTMLhandleScriptlevel(n);return n}});h.TeXAtom.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);n.className="MJXp-mrow";return 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v=[],x=this.FONTDATA.VARIANT;if(t.remap&&t.remap[y]){y=t.remap[y];if(t.remap.variant){t=x[t.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!t.noRemap){y=this.FONTDATA.REMAP[y]}}if(g(y)){if(y[2]){w=n}t=x[y[1]];y=y[0]}if(typeof(y)==="string"){var s={text:y,i:0,length:y.length};while(s.i<s.length){y=this.getUnicode(s);var u=this.getCharList(t,y);if(u){v.push.apply(v,u)}}}else{if(t.cache[y]){v=t.cache[y]}else{t.cache[y]=v=this.lookupChar(t,y,w)}}return v},lookupChar:function(v,z,x){var y=v;while(v){for(var u=0,s=v.fonts.length;u<s;u++){var t=this.FONTDATA.FONTS[v.fonts[u]];if(typeof(t)==="string"){this.loadFont(t)}var w=t[z];if(w){this.fixChar(w,z);if(w[5].space){return[{type:"space",w:w[2],font:t}]}return[{type:"char",font:t,n:z}]}else{if(t.Extra){this.findBlock(t,z)}}}v=this.FONTDATA.VARIANT[v.chain];if(v&&v.remap&&v.remap[z]&&x++<n){return this.remapChar(v,z,x)}}return[this.unknownChar(y,z)]},fixChar:function(s,t){if(s.length===5){s[5]={}}if(s.c==null){s[0]/=1000;s[1]/=1000;s[2]/=1000;s[3]/=1000;s[4]/=1000;s.c=this.unicodeChar(t)}return s},findBlock:function(u,y){var t=u.Extra,v=u.file,x;for(var w=0,s=t.length;w<s;w++){if(typeof(t[w])==="number"){if(y===t[w]){x=v;break}}else{if(y<t[w][0]){return}if(y<=t[w][1]){x=v;break}}}if(x){delete u.Extra;this.loadFont(v)}},unknownChar:function(s,v){f.signal.Post(["CommonHTML Jax - unknown char",v,s]);var u="";if(s.bold){u+="B"}if(s.italic){u+="I"}var t=this.FONTDATA.UNKNOWN[u||"R"];if(!t[v]){this.getUnknownChar(t,v)}return{type:"unknown",n:v,font:t}},getUnknownChar:function(t,v){var u=this.unicodeChar(v);var s=this.getHDW(u,t.className);t[v]=[0.8,0.2,s.w,0,s.w,{a:Math.max(0,(s.h-s.d)/2),h:s.h,d:s.d}];t[v].c=u},styledText:function(t,w){f.signal.Post(["CommonHTML Jax - styled text",w,t]);var u=t.style;var x="_"+(u["font-family"]||t.className||"");if(u["font-weight"]){x+="_"+u["font-weight"]}if(u["font-style"]){x+="_"+u["font-style"]}if(!this.STYLEDTEXT){this.STYLEDTEXT={}}if(!this.STYLEDTEXT[x]){this.STYLEDTEXT[x]={className:t.className||""}}var v=this.STYLEDTEXT[x];if(!v["_"+w]){var s=this.getHDW(w,t.className||"",u);v["_"+w]=[0.8,0.2,s.w,0,s.w,{a:Math.max(0,(s.h-s.d)/2),h:s.h,d:s.d}];v["_"+w].c=w}return{type:"unknown",n:"_"+w,font:v,style:u,rscale:t.rscale}},getHDW:function(B,u,F){var t=a.addElement(a.CHTMLnode,"mjx-chartest",{className:u},[["mjx-char",{style:F},[B]]]);var s=a.addElement(a.CHTMLnode,"mjx-chartest",{className:u},[["mjx-char",{style:F},[B,["mjx-box"]]]]);t.firstChild.style.fontSize=s.firstChild.style.fontSize="";var v=5*a.em;var E=t.offsetHeight,C=s.offsetHeight,x=t.offsetWidth;a.CHTMLnode.removeChild(t);a.CHTMLnode.removeChild(s);if(C===0){v=5*a.defaultEm;var A=document.body.appendChild(document.createElement("div"));A.appendChild(t);A.appendChild(s);E=t.offsetHeight,C=s.offsetHeight,x=t.offsetWidth;document.body.removeChild(A)}var z=(C-1000)/v,D=x/v,y=E/v-z;return{h:y,d:z,w:D}},addCharList:function(v,x,y){var w={text:"",className:null,a:0};for(var t=0,s=x.length;t<s;t++){var u=x[t];if(this.charList[u.type]){(this.charList[u.type])(u,v,y,w,s)}}if(w.text!==""){if(v.childNodes.length){this.charList.flushText(v,w)}else{m.addText(v,w.text);if(v.className){v.className+=" "+w.className}else{v.className=w.className}}}y.b=(w.flushed?0:y.a)},charList:{"char":function(D,x,B,u,y){var w=D.font,A=(w.remapCombining||{})[D.n];if(w.className===u.className){A=null}else{if(u.className||(A&&u.text!=="")){this.flushText(x,u)}}if(!u.a){u.a=w.centerline/1000}if(u.a>(B.a||0)){B.a=u.a}u.className=w.className;var t=w[D.n];if(A){var v=w;if(g(A)){v=a.FONTDATA.FONTS[A[1]];A=A[0];if(typeof(v)==="string"){a.loadFont(v)}}if(v[D.n]){a.fixChar(v[D.n],D.n)}t=a.fixChar(v[A],A);u.className=v.className}u.text+=t.c;if(B.h<t[0]+j){B.t=B.h=t[0]+j}if(B.d<t[1]+b){B.b=B.d=t[1]+b}if(B.l>B.w+t[3]){B.l=B.w+t[3]}if(B.r<B.w+t[4]){B.r=B.w+t[4]}B.w+=t[2]*(D.rscale||1);if(y==1&&w.skew&&w.skew[D.n]){B.skew=w.skew[D.n]}if(t[5]&&t[5].rfix){this.flushText(x,u).style.marginRight=a.Em(t[5].rfix/1000)}if(A){var z=this.flushText(x,u);var s=(v[D.n]||w[D.n])[4]-(t[4]-t[2]);z.style.marginLeft=a.Em(-t[2]-s);if(s<0){z.style.marginRight=a.Em(-s)}}},space:function(t,s,v,u){if(t.w){if(u.text===""){u.className=t.font.className}this.flushText(s,u).style.marginRight=a.Em(t.w);v.w+=t.w}},unknown:function(t,s,w,u){(this["char"])(t,s,w,u,0);var 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B,A,O,v,I,t,F,y,G=1,M;I=this.createChar(N,(P.top||P.ext),1,C);B=N.removeChild(N.firstChild);t=this.createChar(N,(P.bot||P.ext),1,C);A=N.removeChild(N.firstChild);F=y=a.BBOX.zero();var J=I.h+I.d+t.h+t.d-l;E.appendChild(B);if(P.mid){F=this.createChar(N,P.mid,1,C);O=N.removeChild(N.firstChild);J+=F.h+F.d;G=2}if(P.min&&x<J*P.min){x=J*P.min}if(x>J){y=this.createChar(N,P.ext,1,C);v=N.removeChild(N.firstChild);var L=y.h+y.d,u=L-l;var D=Math.min(Math.ceil((x-J)/(G*u)),this.maxStretchyParts);if(P.fullExtenders){x=D*G*u+J}else{u=(x-J)/(G*D)}M=y.d+y.a-L/2;v.style.margin=v.style.padding="";v.style.lineHeight=a.Em(u);v.style.marginBottom=a.Em(M-l/2/G);v.style.marginTop=a.Em(-M-l/2/G);var K=v.textContent,z="\n"+K;while(--D>0){K+=z}v.textContent=K;E.appendChild(v);if(P.mid){E.appendChild(O);E.appendChild(v.cloneNode(true))}}else{M=(x-J-l)/G;B.style.marginBottom=a.Em(M+parseFloat(B.style.marginBottom||"0"));if(P.mid){E.appendChild(O)}A.style.marginTop=a.Em(M+parseFloat(A.style.marginTop||"0"))}E.appendChild(A);var s=a.BBOX({w:Math.max(I.w,y.w,t.w,F.w),l:Math.min(I.l,y.l,t.l,F.l),r:Math.max(I.r,y.r,t.r,F.r),h:x-t.d,d:t.d,t:x-t.d,b:t.d});s.offset=0.5*s.w;if(w){s.scale=w.scale;s.rscale=w.rscale}return s},extendDelimiterH:function(F,s,P,v,D){F=a.addElement(F,"mjx-delim-h");var N=a.Element("span");var t,M,O,u,K,C,x,G,z,H=1;C=this.createChar(N,(P.left||P.rep),1,D);t=N.removeChild(N.firstChild);x=this.createChar(N,(P.right||P.rep),1,D);M=N.removeChild(N.firstChild);z=this.createChar(N,P.rep,1,D);u=N.removeChild(N.firstChild);t.style.marginLeft=a.Em(-C.l);M.style.marginRight=a.Em(x.r-x.w);F.appendChild(t);var 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this.D}}if(u*t.d-v>this.d){this.d=u*t.d-v}if(v+u*t.t>this.t){this.t=v+u*t.t}if(u*t.b-v>this.b){this.b=u*t.b-v}},append:function(t){var u=t.rscale;var s=this.w;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.l<this.l){this.l=s+u*t.l}this.w+=u*(t.w+(t.L||0)+(t.R||0));if(u*t.h>this.h){this.h=u*t.h}if(t.D&&(this.D==null||u*t.D>this.D)&&u*t.D>this.d){this.D=u*t.D}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d>this.d){this.d=u*t.d}if(u*t.t>this.t){this.t=u*t.t}if(u*t.b>this.b){this.b=u*t.b}},updateFrom:function(s){this.h=s.h;this.d=s.d;this.w=s.w;this.r=s.r;this.l=s.l;this.t=s.t;this.b=s.b;if(s.pwidth){this.pwidth=s.pwidth}if(s.D){this.D=s.D}else{delete this.D}},adjust:function(t,s,v,u){this[s]+=a.length2em(t,1,this.scale);if(u==null){if(this[s]>this[v]){this[v]=this[s]}}else{if(this[v]<u){this[v]=u}}}},{zero:function(){return a.BBOX({h:0,d:0,w:0,l:0,r:0,t:0,b:0,scale:1,rscale:1})},empty:function(s){if(!s){s=a.BBOX.zero()}s.h=s.d=s.r=s.t=s.b=-i;s.w=0;s.l=i;delete s.pwidth;return s},styleAdjust:[["borderTopWidth","h","t"],["borderRightWidth","w","r"],["borderBottomWidth","d","b"],["borderLeftWidth","w","l",0],["paddingTop","h","t"],["paddingRight","w","r"],["paddingBottom","d","b"],["paddingLeft","w","l",0],]});MathJax.Hub.Register.StartupHook("mml Jax Ready",function(){d=MathJax.ElementJax.mml;d.mbase.Augment({toCommonHTML:function(t,s){return this.CHTMLdefaultNode(t,s)},CHTMLmultiline:function(){d.mbase.CHTMLautoloadFile("multiline")},CHTMLdefaultNode:function(v,t){if(!t){t={}}v=this.CHTMLcreateNode(v);this.CHTML=a.BBOX.empty();this.CHTMLhandleStyle(v);if(this.isToken){this.CHTMLgetVariant()}this.CHTMLhandleScale(v);var s=Math.max((t.minChildren||0),this.data.length);for(var u=0;u<s;u++){this.CHTMLaddChild(v,u,t)}if(!t.noBBox){this.CHTML.clean()}this.CHTMLhandleSpace(v);this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v},CHTMLaddChild:function(x,t,s){var z=this.data[t],w;var u=s.childNodes;if(u instanceof Array){u=u[t]||"span"}if(z){if(u){x=a.addElement(x,u)}w=z.toCommonHTML(x,s.childOptions);if(u&&z.CHTML.rscale!==1){x.style.fontSize=x.firstChild.style.fontSize;x.firstChild.style.fontSize=""}if(!s.noBBox){var y=this.CHTML,v=z.CHTML;y.append(v);if(this.data.length===1){if(v.ic){y.ic=v.ic}if(v.skew){y.skew=v.skew}}else{delete y.ic;delete y.skew}if(v.pwidth){y.pwidth=v.pwidth}}}else{if(s.forceChild){w=a.addElement(x,(u||"mjx-box"))}}return w},CHTMLchildNode:function(t,s){t=t.childNodes[s];if(t.nodeName.toLowerCase()==="a"){t=t.firstChild}return t},CHTMLcoreNode:function(s){if(this.inferRow&&this.data[0]){return this.data[0].CHTMLcoreNode(s.firstChild)}return this.CHTMLchildNode(s,this.CoreIndex())},CHTMLstretchChildV:function(v,u,y){var x=this.data[v];if(x){var z=this.CHTML,t=x.CHTML;if(t.stretch||(t.stretch==null&&x.CHTMLcanStretch("Vertical",u,y))){var 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u=v.style;u.cssText=this.style;this.removedStyles={};for(var t=0,s=a.removeStyles.length;t<s;t++){var w=a.removeStyles[t];if(u[w]){this.removedStyles[w]=u[w];u[w]=""}}},CHTMLhandleBBox:function(w){var t=this.CHTML,v=w.style;if(this.data.length===1&&(this.data[0].CHTML||{}).pwidth){t.pwidth=this.data[0].CHTML.pwidth;t.mwidth=this.data[0].CHTML.mwidth;v.width="100%"}else{if(t.pwidth){t.mwidth=a.Em(t.w);v.width="100%"}else{if(t.w<0){v.width="0px";v.marginRight=a.Em(t.w)}}}if(!this.style){return}for(var u=0,s=a.BBOX.styleAdjust.length;u<s;u++){var x=a.BBOX.styleAdjust[u];if(x&&v[x[0]]){t.adjust(v[x[0]],x[1],x[2],x[3])}}},CHTMLhandleColor:function(s){if(this.mathcolor){s.style.color=this.mathcolor}else{if(this.color){s.style.color=this.color}}if(this.mathbackground){s.style.backgroundColor=this.mathbackground}else{if(this.background){s.style.backgroundColor=this.background}}},CHTMLhandleSpace:function(s){if(!this.useMMLspacing){var t=this.texSpacing();if(t!==""){this.CHTML.L=this.CHTMLlength2em(t);s.className+=" "+a.SPACECLASS[t]}}},CHTMLhandleText:function(t,u,s){if(t.firstChild&&!this.CHTML){this.CHTML=a.BBOX.empty()}this.CHTML=a.handleText(t,u,s,this.CHTML)},CHTMLgetVariant:function(){var s=this.getValues("mathvariant","fontfamily","fontweight","fontstyle"),u;s.hasVariant=this.Get("mathvariant",true);if(this.removedStyles){u=this.removedStyles;if(u.fontFamily){s.family=u.fontFamily}if(u.fontWeight){s.weight=u.fontWeight}if(u.fontStyle){s.style=u.fontStyle}}if(!s.hasVariant){if(s.fontfamily){s.family=s.fontfamily}if(s.fontweight){s.weight=s.fontweight}if(s.fontstyle){s.style=s.fontstyle}}if(s.weight&&s.weight.match(/^\d+$/)){s.weight=(parseInt(s.weight)>600?"bold":"normal")}var t=s.mathvariant;if(this.variantForm){t="-TeX-variant"}if(s.family&&!s.hasVariant){if(!s.weight&&s.mathvariant.match(/bold/)){s.weight="bold"}if(!s.style&&s.mathvariant.match(/italic/)){s.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":s.family,"font-weight":s.weight||"normal","font-style":s.style||"normal"}};return}if(s.weight==="bold"){t={normal:d.VARIANT.BOLD,italic:d.VARIANT.BOLDITALIC,fraktur:d.VARIANT.BOLDFRAKTUR,script:d.VARIANT.BOLDSCRIPT,"sans-serif":d.VARIANT.BOLDSANSSERIF,"sans-serif-italic":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.weight==="normal"){t={bold:d.VARIANT.normal,"bold-italic":d.VARIANT.ITALIC,"bold-fraktur":d.VARIANT.FRAKTUR,"bold-script":d.VARIANT.SCRIPT,"bold-sans-serif":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.SANSSERIFITALIC}[t]||t}}if(s.style==="italic"){t={normal:d.VARIANT.ITALIC,bold:d.VARIANT.BOLDITALIC,"sans-serif":d.VARIANT.SANSSERIFITALIC,"bold-sans-serif":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.style==="normal"){t={italic:d.VARIANT.NORMAL,"bold-italic":d.VARIANT.BOLD,"sans-serif-italic":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.BOLDSANSSERIF}[t]||t}}this.CHTMLvariant=a.FONTDATA.VARIANT[t]||a.FONTDATA.VARIANT[d.VARIANT.NORMAL]},CHTMLbboxFor:function(s){if(this.data[s]&&this.data[s].CHTML){return this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFile:function(s){var t=a.autoloadDir+"/"+s+".js";f.RestartAfter(o.Require(t))},CHTMLstretchV:function(s,t){this.Core().CHTMLstretchV(s,t);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.chars.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remap){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.entity.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remapchars){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.math.Augment({toCommonHTML:function(x){x=this.CHTMLdefaultNode(x);if(this.CHTML.w<0){x.parentNode.style.width="0px";x.parentNode.style.marginRight=a.Em(this.CHTML.w)}var v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width 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u=this.CHTML,t=this.data.join("");if(u.skew!=null&&t.length!==1){delete u.skew}if(u.r>u.w&&t.length===1&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&t.length!==1){delete u.skew}if(u.r>u.w&&t.length===1&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u<s;u++){this.CHTMLaddChild(v,u,{childOptions:{variant:t.mathvariant,remap:this.remap,remapchars:t.remapchars}})}if(t.text.length!==1){delete this.CHTML.skew}else{if(this.CHTML.w===0&&this.CHTML.l<0){this.CHTMLfixCombiningChar(v)}}if(t.largeop){this.CHTMLcenterOp(v)}}this.CHTML.clean();this.CHTMLhandleBBox(v);this.CHTMLhandleSpace(v);this.CHTMLhandleColor(v);return v},CHTMLhandleSpace:function(v){if(this.useMMLspacing){var t=this.getValues("scriptlevel","lspace","rspace");t.lspace=Math.max(0,this.CHTMLlength2em(t.lspace));t.rspace=Math.max(0,this.CHTMLlength2em(t.rspace));if(t.scriptlevel>0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var 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M=a.TEX.rule_thickness;if((L-w*W.d)-(B*P.h-J)<3*M){J=3*M-L+w*W.d+B*P.h;Q=(4/5)*X-(L-w*W.d);if(Q>0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var 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