* 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.
*/
(function(b,d){vari="2.7.0";vara="http://www.stixfonts.org/";varf="https://github.com/mathjax/MathJax/tree/master/fonts/HTML-CSS/TeX/otf";varh=b.CombineConfig("FontWarnings",{messageStyle:{position:"fixed",bottom:"4em",left:"3em",width:"40em",border:"3px solid #880000","background-color":"#E0E0E0",color:"black",padding:"1em","font-size":"small","white-space":"normal","border-radius":".75em","-webkit-border-radius":".75em","-moz-border-radius":".75em","-khtml-border-radius":".75em","box-shadow":"4px 4px 10px #AAAAAA","-webkit-box-shadow":"4px 4px 10px #AAAAAA","-moz-box-shadow":"4px 4px 10px #AAAAAA","-khtml-box-shadow":"4px 4px 10px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=3, OffY=3, Color='gray', Positive='true')"},Message:{webFont:[["closeBox"],["webFont","MathJax is using web-based fonts to display the mathematics on this page. These take time to download, so the page would render faster if you installed math fonts directly in your system's font folder."],["fonts"]],imageFonts:[["closeBox"],["imageFonts","MathJax is using its image fonts rather than local or web-based fonts. This will render slower than usual, and the mathematics may not print at the full resolution of your printer."],["fonts"],["webFonts"]],noFonts:[["closeBox"],["noFonts","MathJax is unable to locate a font to use to display its mathematics, and image fonts are not available, so it is falling back on generic unicode characters in hopes that your browser will be able to display them. Some characters may not show up properly, or possibly not at all."],["fonts"],["webFonts"]]},HTML:{closeBox:[["div",{style:{position:"absolute",overflow:"hidden",top:".1em",right:".1em",border:"1px outset",width:"1em",height:"1em","text-align":"center",cursor:"pointer","background-color":"#EEEEEE",color:"#606060","border-radius":".5em","-webkit-border-radius":".5em","-moz-border-radius":".5em","-khtml-border-radius":".5em"},onclick:function(){if(c.div&&c.fade===0){if(c.timer){clearTimeout(c.timer)}c.div.style.display="none"}}},[["span",{style:{position:"relative",bottom:".2em"}},["x"]]]]],webFonts:[["p"],["webFonts","Most modern browsers allow for fonts to be downloaded over the web. Updating to a more recent version of your browser (or changing browsers) could improve the quality of the mathematics on this page."]],fonts:[["p"],["fonts","MathJax can use either the [STIX fonts](%1) or the [MathJax TeX fonts](%2). Download and install one of those fonts to improve your MathJax experience.",a,f]],STIXfonts:[["p"],["STIXPage","This page is designed to use the [STIX fonts](%1). Download and install those fonts to improve your MathJax experience.",a]],TeXfonts:[["p"],["TeXPage","This page is designed to use the [MathJax TeX fonts](%1). Download and install those fonts to improve your MathJax experience.",f]]},removeAfter:12*1000,fadeoutSteps:10,fadeoutTime:1.5*1000});if(MathJax.Hub.Browser.isIE9&&document.documentMode>=9){deleteh.messageStyle.filter}varc={div:null,fade:0};vare=function(m){if(c.div){return}varj=MathJax.OutputJax["HTML-CSS"],n=document.body;if(b.Browser.isMSIE){if(h.messageStyle.position==="fixed"){MathJax.Message.Init();n=document.getElementById("MathJax_MSIE_Frame")||n;if(n!==document.body){h.messageStyle.position="absolute"}}}else{deleteh.messageStyle.filter}h.messageStyle.maxWidth=(document.body.clientWidth-75)+"px";vark=0;while(k<m.length){if(MathJax.Object.isArray(m[k])){if(m[k].length===1&&h.HTML[m[k][0]]){m.splice.apply(m,[k,1].concat(h.HTML[m[k][0]]))}else{if(typeofm[k][1]==="string"){varl=MathJax.Localization.lookupPhrase(["FontWarnings",m[k][0]],m[k][1]);l=MathJax.Localization.processMarkdown(l,m[k].slice(2),"FontWarnings");m.splice.apply(m,[k,1].concat(l));k+=l.length}else{k++}}}else{k++}}c.div=j.addElement(n,"div",{id:"MathJax_FontWarning",style:h.messageStyle},m);MathJax.Localization.setCSS(c.div);if(h.removeAfter){b.Register.StartupHook("End",function(){c.timer=setTimeout(g,h.removeAfter)})}d.Cookie.Set("fontWarn",{warned:true})};varg=function(){c.fade++;if(c.timer){deletec.timer}if(c.fade<h.fadeoutSteps){varj=1-c.fade/h.fadeoutSteps;c.div.style.opacity=j;c.div.style.filter="alpha(opacity="+Math.floor(100*j)+")";setTimeout(g,h.fadeoutTime/h.fadeoutSteps)}else{c.div.style.display="none"}};if(!d.Cookie.Get("fontWarn").warned){b.Startup.signal.Interest(function(m){if(m.match(/HTML-CSS Jax - /)&&!c.div){varj=MathJax.OutputJax["HTML-CSS"],n=j.config.availableFonts,l;vark=(n&&n.length);if(!k){h.HTML.fonts=[""]}else{if(n.length===1){h.HTML.fonts=h.HTML[n[0]+"fonts"]}}if(j.allowWebFonts){h.HTML.webfonts=[""]}if(m.match(/- Web-Font/)){if(k){l="webFont"}}else{if(m.match(/- using image fonts/)){l="imageFonts"}else{if(m.match(/- no valid font/)){l="noFonts"}}}if(l&&h.Message[l]){MathJax.Localization.loadDomain("FontWarnings",[e,h.Message[l]])}}})}})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/FontWarnings.js");
* 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.
*/
(function(d,f,i,c,j){vare=MathJax.Extension.Help={version:"2.7.0"};varb="http://www.stixfonts.org/";vara=MathJax.Menu;varh,g;d.Register.StartupHook("MathEvents Ready",function(){h=MathJax.Extension.MathEvents.Event.False;g=MathJax.Extension.MathEvents.Event.KEY});vark=d.CombineConfig("HelpDialog",{styles:{"#MathJax_Help":{position:"fixed",left:"50%",width:"auto","max-width":"90%","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":"wrap","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_Help.MathJax_MousePost":{outline:"none"},"#MathJax_HelpContent":{overflow:"auto","text-align":"left","font-size":"80%",padding:".4em .6em",border:"1px inset",margin:"1em 0px","max-height":"20em","max-width":"30em","background-color":"#EEEEEE"},"#MathJax_HelpClose":{position:"absolute",top:".2em",right:".2em",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},"#MathJax_HelpClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},"#MathJax_HelpClose:hover":{color:"white!important",border:"2px solid #CCC!important"},"#MathJax_HelpClose:hover span":{"background-color":"#CCC!important"},"#MathJax_HelpClose:hover:focus":{outline:"none"}}});e.Dialog=function(l){j.loadDomain("HelpDialog",["Post",e,l])};e.Post=function(n){this.div=a.Background(this);varl=f.addElement(this.div,"div",{id:"MathJax_Help",tabIndex:0,onkeydown:e.Keydown},j._("HelpDialog",[["b",{style:{fontSize:"120%"}},[["Help","MathJax Help"]]],["div",{id:"MathJax_HelpContent",tabIndex:0},[["p",{},[["MathJax","*MathJax* is a JavaScript library that allows page authors to include mathematics within their web pages. As a reader, you don't need to do anything to make that happen."]]],["p",{},[["Browsers","*Browsers*: MathJax works with all modern browsers including IE6+, Firefox 3+, Chrome 0.2+, Safari 2+, Opera 9.6+ and most mobile browsers."]]],["p",{},[["Menu","*Math Menu*: MathJax adds a contextual menu to equations. Right-click or CTRL-click on any mathematics to access the menu."]]],["div",{style:{"margin-left":"1em"}},[["p",{},[["ShowMath","*Show Math As* allows you to view the formula's source markup for copy & paste (as MathML or in its original format)."]]],["p",{},[["Settings","*Settings* gives you control over features of MathJax, such as the size of the mathematics, and the mechanism used to display equations."]]],["p",{},[["Language","*Language* lets you select the language used by MathJax for its menus and warning messages."]]],]],["p",{},[["Zoom","*Math Zoom*: If you are having difficulty reading an equation, MathJax can enlarge it to help you see it better."]]],["p",{},[["Accessibilty","*Accessibility*: MathJax will automatically work with screen readers to make mathematics accessible to the visually impaired."]]],["p",{},[["Fonts","*Fonts*: MathJax will use certain math fonts if they are installed on your computer; otherwise, it will use web-based fonts. Although not required, locally installed fonts will speed up typesetting. We suggest installing the [STIX fonts](%1).",b]]]]],["a",{href:"http://www.mathjax.org/"},["www.mathjax.org"]],["span",{id:"MathJax_HelpClose",onclick:e.Remove,onkeydown:e.Keydown,tabIndex:0,role:"button","aria-label":j._(["HelpDialog","CloseDialog"],"Close help dialog")},[["span",{},["\u00D7"]]]]]));if(n.type==="mouseup"){l.className+=" MathJax_MousePost"}l.focus();j.setCSS(l);varo=(document.documentElement||{});varm=window.innerHeight||o.clientHeight||o.scrollHeight||0;if(a.prototype.msieAboutBug){l.style.width="20em";l.style.position="absolute";l.style.left=Math.floor((document.documentElement.scrollWidth-l.offsetWidth)/2)+"px";l.style.top=(Math.floor((m-l.offsetHeight)/3)+document.body.scrollTop)+"px"}else{l.style.marginLeft=Math.floor(-l.offsetWidth/2)+"px";l.style.top=Math.floor((m-l.offsetHeight)/3)+"px"}};e.Remove=function(l){if(e.div){document.body.removeChild(e.div);deletee.div}};e.Keydown=function(l){if(l.keyCode===g.ESCAPE||(this.id==="MathJax_HelpClose"&&(l.keyCode===g.SPACE||l.keyCode===g.RETURN))){e.Remove(l);a.CurrentNode().focus();h(l)}},MathJax.Callback.Queue(d.Register.StartupHook("End Config",{}),["Styles",i,k.styles],["Post",d.Startup.signal,"HelpDialig Ready"],["loadComplete",i,"[MathJax]/extensions/HelpDialog.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax,MathJax.Localization);
* 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.
*/
MathJax.Extension["TeX/AMSmath"]={version:"2.7.0",number:0,startNumber:0,IDs:{},eqIDs:{},labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){varb=MathJax.ElementJax.mml,h=MathJax.InputJax.TeX,g=MathJax.Extension["TeX/AMSmath"];vard=h.Definitions,f=h.Stack.Item,a=h.config.equationNumbers;varc=function(k){varn=[];for(varl=0,j=k.length;l<j;l++){n[l]=h.Parse.prototype.Em(k[l])}returnn.join("")};vare=(document.getElementsByTagName("base").length===0)?"":String(document.location).replace(/#.*$/,"");d.Add({mathchar0mo:{iiiint:["2A0C",{texClass:b.TEXCLASS.OP}]},macros:{mathring:["Accent","2DA"],nobreakspace:"Tilde",negmedspace:["Spacer",b.LENGTH.NEGATIVEMEDIUMMATHSPACE],negthickspace:["Spacer",b.LENGTH.NEGATIVETHICKMATHSPACE],idotsint:["MultiIntegral","\\int\\cdots\\int"],dddot:["Accent","20DB"],ddddot:["Accent","20DC"],sideset:["Macro","\\mathop{\\mathop{\\rlap{\\phantom{#3}}}\\nolimits#1\\!\\mathop{#3}\\nolimits#2}",3],boxed:["Macro","\\fbox{$\\displaystyle{#1}$}",1],tag:"HandleTag",notag:"HandleNoTag",label:"HandleLabel",ref:"HandleRef",eqref:["HandleRef",true],substack:["Macro","\\begin{subarray}{c}#1\\end{subarray}",1],injlim:["NamedOp","inj lim"],projlim:["NamedOp","proj lim"],varliminf:["Macro","\\mathop{\\underline{\\mmlToken{mi}{lim}}}"],varlimsup:["Macro","\\mathop{\\overline{\\mmlToken{mi}{lim}}}"],varinjlim:["Macro","\\mathop{\\underrightarrow{\\mmlToken{mi}{lim}}}"],varprojlim:["Macro","\\mathop{\\underleftarrow{\\mmlToken{mi}{lim}}}"],DeclareMathOperator:"HandleDeclareOp",operatorname:"HandleOperatorName",SkipLimits:"SkipLimits",genfrac:"Genfrac",frac:["Genfrac","","","",""],tfrac:["Genfrac","","","",1],dfrac:["Genfrac","","","",0],binom:["Genfrac","(",")","0",""],tbinom:["Genfrac","(",")","0",1],dbinom:["Genfrac","(",")","0",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([0,2,0,2,0,2,0,2,0,2,0])],"align*":["AMSarray",null,false,true,"rlrlrlrlrlrl",c([0,2,0,2,0,2,0,2,0,2,0])],multline:["Multline",null,true],"multline*":["Multline",null,false],split:["AMSarray",null,false,false,"rl",c([0])],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:["AlignedAMSArray",null,null,null,"rlrlrlrlrlrl",c([0,2,0,2,0,2,0,2,0,2,0]),".5em","D"],gathered:["AlignedAMSArray",null,null,null,"c",null,".5em","D"],subarray:["Array",null,null,null,null,c([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","0 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rows within the %1 environment must have exactly one 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