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jax.js

jax.js 48 KB
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  1. /*
    2. 

  2.  *  /MathJax/jax/input/TeX/jax.js
    3. 

  3.  *  
    4. 

  4.  *  Copyright (c) 2009-2013 The MathJax Consortium
    5. 

  5.  *
    6. 

  6.  *  Part of the MathJax library.
    7. 

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

  8.  * 
    9. 

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

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

  11.  *
    12. 

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

  13.  */
    14. 

  14. 

  15. (function(d,c,i){var h,g="\u00A0";var j=function(l){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",l]].concat([].slice.call(arguments,1)))};var e=MathJax.Object.Subclass({Init:function(m,l){this.global={isInner:l};this.data=[b.start(this.global)];if(m){this.data[0].env=m}this.env=this.data[0].env},Push:function(){var n,l,o,p;for(n=0,l=arguments.length;n<l;n++){o=arguments[n];if(o instanceof h.mbase){o=b.mml(o)}o.global=this.global;p=(this.data.length?this.Top().checkItem(o):true);if(p instanceof Array){this.Pop();this.Push.apply(this,p)}else{if(p instanceof b){this.Pop();this.Push(p)}else{if(p){this.data.push(o);if(o.env){for(var q in this.env){if(this.env.hasOwnProperty(q)){o.env[q]=this.env[q]}}this.env=o.env}else{o.env=this.env}}}}}},Pop:function(){var l=this.data.pop();if(!l.isOpen){delete l.env}this.env=(this.data.length?this.Top().env:{});return l},Top:function(l){if(l==null){l=1}if(this.data.length<l){return null}return this.data[this.data.length-l]},Prev:function(l){var m=this.Top();if(l){return m.data[m.data.length-1]}else{return m.Pop()}},toString:function(){return"stack[\n  "+this.data.join("\n  ")+"\n]"}});var b=e.Item=MathJax.Object.Subclass({type:"base",endError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],closeError:["ExtraCloseMissingOpen","Extra close brace or missing open brace"],rightError:["MissingLeftExtraRight","Missing \\left or extra \\right"],Init:function(){if(this.isOpen){this.env={}}this.data=[];this.Push.apply(this,arguments)},Push:function(){this.data.push.apply(this.data,arguments)},Pop:function(){return this.data.pop()},mmlData:function(l,m){if(l==null){l=true}if(this.data.length===1&&!m){return this.data[0]}return h.mrow.apply(h,this.data).With((l?{inferred:true}:{}))},checkItem:function(l){if(l.type==="over"&&this.isOpen){l.num=this.mmlData(false);this.data=[]}if(l.type==="cell"&&this.isOpen){if(l.linebreak){return false}d.Error(["Misplaced","Misplaced %1",l.name])}if(l.isClose&&this[l.type+"Error"]){d.Error(this[l.type+"Error"])}if(!l.isNotStack){return true}this.Push(l.data[0]);return false},With:function(l){for(var m in l){if(l.hasOwnProperty(m)){this[m]=l[m]}}return this},toString:function(){return this.type+"["+this.data.join("; ")+"]"}});b.start=b.Subclass({type:"start",isOpen:true,Init:function(l){this.SUPER(arguments).Init.call(this);this.global=l},checkItem:function(l){if(l.type==="stop"){return b.mml(this.mmlData())}return this.SUPER(arguments).checkItem.call(this,l)}});b.stop=b.Subclass({type:"stop",isClose:true});b.open=b.Subclass({type:"open",isOpen:true,stopError:["ExtraOpenMissingClose","Extra open brace or missing close brace"],checkItem:function(m){if(m.type==="close"){var l=this.mmlData();return b.mml(h.TeXAtom(l))}return this.SUPER(arguments).checkItem.call(this,m)}});b.close=b.Subclass({type:"close",isClose:true});b.prime=b.Subclass({type:"prime",checkItem:function(l){if(this.data[0].type!=="msubsup"){return[h.msup(this.data[0],this.data[1]),l]}this.data[0].SetData(this.data[0].sup,this.data[1]);return[this.data[0],l]}});b.subsup=b.Subclass({type:"subsup",stopError:["MissingScript","Missing superscript or subscript argument"],supError:["MissingOpenForSup","Missing open brace for superscript"],subError:["MissingOpenForSup","Missing open brace for subscript"],checkItem:function(l){if(l.type==="open"||l.type==="left"){return true}if(l.type==="mml"){if(this.primes){if(this.position!==2){this.data[0].SetData(2,this.primes)}else{l.data[0]=h.mrow(this.primes.With({variantForm:true}),l.data[0])}}this.data[0].SetData(this.position,l.data[0]);return b.mml(this.data[0])}if(this.SUPER(arguments).checkItem.call(this,l)){d.Error(this[["","subError","supError"][this.position]])}},Pop:function(){}});b.over=b.Subclass({type:"over",isClose:true,name:"\\over",checkItem:function(n,l){if(n.type==="over"){d.Error(["AmbiguousUseOf","Ambiguous use of %1",n.name])}if(n.isClose){var m=h.mfrac(this.num,this.mmlData(false));if(this.thickness!=null){m.linethickness=this.thickness}if(this.open||this.close){m.texClass=h.TEXCLASS.INNER;m.texWithDelims=true;m=d.fenced(this.open,m,this.close)}return[b.mml(m),n]}return this.SUPER(arguments).checkItem.call(this,n)},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(l){if(l.type==="right"){return b.mml(d.fenced(this.delim,this.mmlData(),l.delim))}return this.SUPER(arguments).checkItem.call(this,l)}});b.right=b.Subclass({type:"right",isClose:true,delim:")"});b.begin=b.Subclass({type:"begin",isOpen:true,checkItem:function(l){if(l.type==="end"){if(l.name!==this.name){d.Error(["EnvBadEnd","\\begin{%1} ended with \\end{%2}",this.name,l.name])}if(!this.end){return b.mml(this.mmlData())}return this.parse[this.end].call(this.parse,this,this.data)}if(l.type==="stop"){d.Error(["EnvMissingEnd","Missing \\end{%1}",this.name])}return this.SUPER(arguments).checkItem.call(this,l)}});b.end=b.Subclass({type:"end",isClose:true});b.style=b.Subclass({type:"style",checkItem:function(m){if(!m.isClose){return this.SUPER(arguments).checkItem.call(this,m)}var l=h.mstyle.apply(h,this.data).With(this.styles);return[b.mml(l),m]}});b.position=b.Subclass({type:"position",checkItem:function(m){if(m.isClose){d.Error(["MissingBoxFor","Missing box for %1",name])}if(m.isNotStack){var l=m.mmlData();switch(this.move){case"vertical":l=h.mpadded(l).With({height:this.dh,depth:this.dd,voffset:this.dh});return[b.mml(l)];case"horizontal":return[b.mml(this.left),m,b.mml(this.right)]}}return this.SUPER(arguments).checkItem.call(this,m)}});b.array=b.Subclass({type:"array",isOpen:true,arraydef:{},Init:function(){this.table=[];this.row=[];this.env={};this.frame=[];this.SUPER(arguments).Init.apply(this,arguments)},checkItem:function(m){if(m.isClose&&m.type!=="over"){if(m.isEntry){this.EndEntry();this.clearEnv();return false}if(m.isCR){this.EndEntry();this.EndRow();this.clearEnv();return false}this.EndTable();this.clearEnv();var l=h.mtable.apply(h,this.table).With(this.arraydef);if(this.frame.length===4){l.frame=(this.frame.dashed?"dashed":"solid")}else{if(this.frame.length){l.hasFrame=true;if(this.arraydef.rowlines){this.arraydef.rowlines=this.arraydef.rowlines.replace(/none( none)+$/,"none")}l=h.menclose(l).With({notation:this.frame.join(" "),isFrame:true});if((this.arraydef.columnlines||"none")!="none"||(this.arraydef.rowlines||"none")!="none"){l.padding=0}}}if(this.open||this.close){l=d.fenced(this.open,l,this.close)}l=b.mml(l);if(this.requireClose){if(m.type==="close"){return l}d.Error(["MissingCloseBrace","Missing close brace"])}return[l,m]}return this.SUPER(arguments).checkItem.call(this,m)},EndEntry:function(){this.row.push(h.mtd.apply(h,this.data));this.data=[]},EndRow:function(){this.table.push(h.mtr.apply(h,this.row));this.row=[]},EndTable:function(){if(this.data.length||this.row.length){this.EndEntry();this.EndRow()}this.checkLines()},checkLines:function(){if(this.arraydef.rowlines){var l=this.arraydef.rowlines.split(/ /);if(l.length===this.table.length){this.frame.push("bottom");l.pop();this.arraydef.rowlines=l.join(" ")}else{if(l.length<this.table.length-1){this.arraydef.rowlines+=" none"}}}if(this.rowspacing){var m=this.arraydef.rowspacing.split(/ /);while(m.length<this.table.length){m.push(this.rowspacing+"em")}this.arraydef.rowspacing=m.join(" ")}},clearEnv:function(){for(var l in this.env){if(this.env.hasOwnProperty(l)){delete this.env[l]}}}});b.cell=b.Subclass({type:"cell",isClose:true});b.mml=b.Subclass({type:"mml",isNotStack:true,Add:function(){this.data.push.apply(this.data,arguments);return this}});b.fn=b.Subclass({type:"fn",checkItem:function(m){if(this.data[0]){if(m.type!=="mml"||!m.data[0]){return[this.data[0],m]}if(m.data[0].isa(h.mspace)){return[this.data[0],m]}var l=m.data[0];if(l.isEmbellished()){l=l.CoreMO()}if([0,0,1,1,0,1,1,0,0,0][l.Get("texClass")]){return[this.data[0],m]}return[this.data[0],h.mo(h.entity("#x2061")).With({texClass:h.TEXCLASS.NONE}),m]}return this.SUPER(arguments).checkItem.apply(this,arguments)}});b.not=b.Subclass({type:"not",checkItem:function(m){var l,n;if(m.type==="open"||m.type==="left"){return true}if(m.type==="mml"&&m.data[0].type.match(/^(mo|mi|mtext)$/)){l=m.data[0],n=l.data.join("");if(n.length===1&&!l.movesupsub){n=b.not.remap[n.charCodeAt(0)];if(n){l.SetData(0,h.chars(String.fromCharCode(n)))}else{l.Append(h.chars("\u0338"))}return m}}l=h.mpadded(h.mtext("\u29F8")).With({width:0});l=h.TeXAtom(l).With({texClass:h.TEXCLASS.REL});return[l,m]}});b.not.remap={8592:8602,8594:8603,8596:8622,8656:8653,8658:8655,8660:8654,8712:8713,8715:8716,8739:8740,8741:8742,8764:8769,126:8769,8771:8772,8773:8775,8776:8777,8781:8813,61:8800,8801:8802,60:8814,62:8815,8804:8816,8805:8817,8818:8820,8819:8821,8822:8824,8823:8825,8826:8832,8827:8833,8834:8836,8835:8837,8838:8840,8839:8841,8866:8876,8872:8877,8873:8878,8875:8879,8828:8928,8829:8929,8849:8930,8850:8931,8882:8938,8883:8939,8884:8940,8885:8941,8707:8708};b.dots=b.Subclass({type:"dots",checkItem:function(m){if(m.type==="open"||m.type==="left"){return true}var n=this.ldots;if(m.type==="mml"&&m.data[0].isEmbellished()){var 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m},Comment:function(l){while(this.i<this.string.length&&this.string.charAt(this.i)!="\n"){this.i++}},Hash:function(l){d.Error(["CantUseHash1","You can't use 'macro parameter character #' in math mode"])},Other:function(n){var m={stretchy:false},l;if(this.stack.env.font){m.mathvariant=this.stack.env.font}if(f.remap[n]){n=f.remap[n];if(n instanceof Array){m=n[1];n=n[0]}l=h.mo(h.entity("#x"+n)).With(m)}else{l=h.mo(n).With(m)}if(l.autoDefault("texClass",true)==""){l=h.TeXAtom(l)}this.Push(this.mmlToken(l))},SetFont:function(m,l){this.stack.env.font=l},SetStyle:function(m,l,n,o){this.stack.env.style=l;this.stack.env.level=o;this.Push(b.style().With({styles:{displaystyle:n,scriptlevel:o}}))},SetSize:function(l,m){this.stack.env.size=m;this.Push(b.style().With({styles:{mathsize:m+"em"}}))},Color:function(n){var m=this.GetArgument(n);var l=this.stack.env.color;this.stack.env.color=m;var o=this.ParseArg(n);if(l){this.stack.env.color}else{delete this.stack.env.color}this.Push(h.mstyle(o).With({mathcolor:m}))},Spacer:function(l,m){this.Push(h.mspace().With({width:m,mathsize:h.SIZE.NORMAL,scriptlevel:0}))},LeftRight:function(l){this.Push(b[l.substr(1)]().With({delim:this.GetDelimiter(l)}))},Middle:function(l){var m=this.GetDelimiter(l);if(this.stack.Top().type!=="left"){d.Error(["MisplacedMiddle","%1 must be within \\left and \\right",l])}this.Push(h.mo(m).With({stretchy:true}))},NamedFn:function(m,n){if(!n){n=m.substr(1)}var l=h.mi(n).With({texClass:h.TEXCLASS.OP});this.Push(b.fn(this.mmlToken(l)))},NamedOp:function(m,n){if(!n){n=m.substr(1)}n=n.replace(/&thinsp;/,"\u2006");var l=h.mo(n).With({movablelimits:true,movesupsub:true,form:h.FORM.PREFIX,texClass:h.TEXCLASS.OP});l.useMMLspacing&=~l.SPACE_ATTR.form;this.Push(this.mmlToken(l))},Limits:function(m,l){var n=this.stack.Prev("nopop");if(!n||n.texClass!==h.TEXCLASS.OP){d.Error(["MisplacedLimits","%1 is allowed only on operators",m])}n.movesupsub=(l?true:false);n.movablelimits=false},Over:function(n,m,o){var l=b.over().With({name:n});if(m||o){l.open=m;l.close=o}else{if(n.match(/withdelims$/)){l.open=this.GetDelimiter(n);l.close=this.GetDelimiter(n)}}if(n.match(/^\\above/)){l.thickness=this.GetDimen(n)}else{if(n.match(/^\\atop/)||m||o){l.thickness=0}}this.Push(l)},Frac:function(m){var l=this.ParseArg(m);var n=this.ParseArg(m);this.Push(h.mfrac(l,n))},Sqrt:function(o){var p=this.GetBrackets(o),l=this.GetArgument(o);if(l==="\\frac"){l+="{"+this.GetArgument(l)+"}{"+this.GetArgument(l)+"}"}var m=d.Parse(l,this.stack.env).mml();if(!p){m=h.msqrt.apply(h,m.array())}else{m=h.mroot(m,this.parseRoot(p))}this.Push(m)},Root:function(m){var o=this.GetUpTo(m,"\\of");var l=this.ParseArg(m);this.Push(h.mroot(l,this.parseRoot(o)))},parseRoot:function(q){var m=this.stack.env,l=m.inRoot;m.inRoot=true;var p=d.Parse(q,m);q=p.mml();var o=p.stack.global;if(o.leftRoot||o.upRoot){q=h.mpadded(q);if(o.leftRoot){q.width=o.leftRoot}if(o.upRoot){q.voffset=o.upRoot;q.height=o.upRoot}}m.inRoot=l;return q},MoveRoot:function(l,o){if(!this.stack.env.inRoot){d.Error(["MisplacedMoveRoot","%1 can appear only within a root",l])}if(this.stack.global[o]){d.Error(["MultipleMoveRoot","Multiple use of %1",l])}var m=this.GetArgument(l);if(!m.match(/-?[0-9]+/)){d.Error(["IntegerArg","The argument to %1 must be an integer",l])}m=(m/15)+"em";if(m.substr(0,1)!=="-"){m="+"+m}this.stack.global[o]=m},Accent:function(n,l,q){var p=this.ParseArg(n);var o={accent:true};if(this.stack.env.font){o.mathvariant=this.stack.env.font}var m=this.mmlToken(h.mo(h.entity("#x"+l)).With(o));m.stretchy=(q?true:false);this.Push(h.TeXAtom(h.munderover(p,null,m).With({accent:true})))},UnderOver:function(n,q,l){var p={o:"over",u:"under"}[n.charAt(1)];var o=this.ParseArg(n);if(o.Get("movablelimits")){o.movablelimits=false}var m=h.munderover(o,null,null);if(l){m.movesupsub=true}m.data[m[p]]=this.mmlToken(h.mo(h.entity("#x"+q)).With({stretchy:true,accent:(p=="under")}));this.Push(m)},Overset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.mover(m,n))},Underset:function(l){var n=this.ParseArg(l),m=this.ParseArg(l);this.Push(h.munder(m,n))},TeXAtom:function(o,q){var p={texClass:q},n;if(q==h.TEXCLASS.OP){p.movesupsub=p.movablelimits=true;var l=this.GetArgument(o);var m=l.match(/^\s*\\rm\s+([a-zA-Z0-9 ]+)$/);if(m){p.mathvariant=h.VARIANT.NORMAL;n=b.fn(this.mmlToken(h.mi(m[1]).With(p)))}else{n=b.fn(h.TeXAtom(d.Parse(l,this.stack.env).mml()).With(p))}}else{n=h.TeXAtom(this.ParseArg(o)).With(p)}this.Push(n)},MmlToken:function(n){var o=this.GetArgument(n),l=this.GetBrackets(n,"").replace(/^\s+/,""),r=this.GetArgument(n),q={attrNames:[]},m;if(!h[o]||!h[o].prototype.isToken){d.Error(["NotMathMLToken","%1 is not a token element",o])}while(l!==""){m=l.match(/^([a-z]+)\s*=\s*(\'[^']*'|"[^"]*"|[^ 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l=h.mpadded(this.ParseArg(n));switch(m){case"b":l.depth=0;break;case"t":l.height=0;break;default:l.height=l.depth=0}this.Push(h.TeXAtom(l))},Lap:function(m){var l=h.mpadded(this.ParseArg(m)).With({width:0});if(m==="\\llap"){l.lspace="-1 width"}this.Push(h.TeXAtom(l))},RaiseLower:function(l){var m=this.GetDimen(l);var n=b.position().With({name:l,move:"vertical"});if(m.charAt(0)==="-"){m=m.slice(1);l={raise:"\\lower",lower:"\\raise"}[l.substr(1)]}if(l==="\\lower"){n.dh="-"+m;n.dd="+"+m}else{n.dh="+"+m;n.dd="-"+m}this.Push(n)},MoveLeftRight:function(l){var o=this.GetDimen(l);var n=(o.charAt(0)==="-"?o.slice(1):"-"+o);if(l==="\\moveleft"){var m=o;o=n;n=m}this.Push(b.position().With({name:l,move:"horizontal",left:h.mspace().With({width:o,mathsize:h.SIZE.NORMAL}),right:h.mspace().With({width:n,mathsize:h.SIZE.NORMAL})}))},Hskip:function(l){this.Push(h.mspace().With({width:this.GetDimen(l),mathsize:h.SIZE.NORMAL}))},Rule:function(n,p){var l=this.GetDimen(n),o=this.GetDimen(n),r=this.GetDimen(n);var m,q={width:l,height:o,depth:r};if(p!=="blank"){if(parseFloat(l)&&parseFloat(o)+parseFloat(r)){q.mathbackground=(this.stack.env.color||"black")}m=h.mpadded(h.mrow()).With(q)}else{m=h.mspace().With(q)}this.Push(m)},MakeBig:function(l,o,m){m*=f.p_height;m=String(m).replace(/(\.\d\d\d).+/,"$1")+"em";var n=this.GetDelimiter(l);this.Push(h.TeXAtom(h.mo(n).With({minsize:m,maxsize:m,fence:true,stretchy:true,symmetric:true})).With({texClass:o}))},BuildRel:function(l){var m=this.ParseUpTo(l,"\\over");var n=this.ParseArg(l);this.Push(h.TeXAtom(h.munderover(n,null,m)).With({mclass:h.TEXCLASS.REL}))},HBox:function(l,m){this.Push.apply(this,this.InternalMath(this.GetArgument(l),m))},FBox:function(l){this.Push(h.menclose.apply(h,this.InternalMath(this.GetArgument(l))).With({notation:"box"}))},Not:function(l){this.Push(b.not())},Dots:function(l){this.Push(b.dots().With({ldots:this.mmlToken(h.mo(h.entity("#x2026")).With({stretchy:false})),cdots:this.mmlToken(h.mo(h.entity("#x22EF")).With({stretchy:false}))}))},Require:function(l){var m=this.GetArgument(l).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");this.Extension(null,m)},Extension:function(l,m,n){if(l&&!typeof(l)==="string"){l=l.name}m=d.extensionDir+"/"+m;if(!m.match(/\.js$/)){m+=".js"}if(!i.loaded[i.fileURL(m)]){if(l!=null){delete f[n||"macros"][l.replace(/^\\/,"")]}c.RestartAfter(i.Require(m))}},Macro:function(n,q,p,r){if(p){var m=[];if(r!=null){var l=this.GetBrackets(n);m.push(l==null?r:l)}for(var o=m.length;o<p;o++){m.push(this.GetArgument(n))}q=this.SubstituteArgs(m,q)}this.string=this.AddArgs(q,this.string.slice(this.i));this.i=0;if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(m,o,t,q,s,n,l,u){var r=this.GetNext();if(r===""){d.Error(["MissingArgFor","Missing argument for %1",m])}if(r==="{"){this.i++}else{this.string=r+"}"+this.string.slice(this.i+1);this.i=0}var p=b.array().With({requireClose:true,arraydef:{rowspacing:(n||"4pt"),columnspacing:(s||"1em")}});if(u){p.isCases=true}if(o||t){p.open=o;p.close=t}if(l==="D"){p.arraydef.displaystyle=true}if(q!=null){p.arraydef.columnalign=q}this.Push(p)},Entry:function(o){this.Push(b.cell().With({isEntry:true,name:o}));if(this.stack.Top().isCases){var n=this.string;var r=0,p=this.i,l=n.length;while(p<l){var s=n.charAt(p);if(s==="{"){r++;p++}else{if(s==="}"){if(r===0){l=0}else{r--;p++}}else{if(s==="&"&&r===0){d.Error(["ExtraAlignTab","Extra alignment tab in \\cases text"])}else{if(s==="\\"){if(n.substr(p).match(/^((\\cr)[^a-zA-Z]|\\\\)/)){l=0}else{p+=2}}else{p++}}}}}var q=n.substr(this.i,p-this.i);if(!q.match(/^\s*\\text[^a-zA-Z]/)){this.Push.apply(this,this.InternalMath(q));this.i=p}}},Cr:function(l){this.Push(b.cell().With({isCR:true,name:l}))},CrLaTeX:function(l){var p;if(this.string.charAt(this.i)==="["){p=this.GetBrackets(l,"").replace(/ /g,"");if(p&&!p.match(/^((-?(\.\d+|\d+(\.\d*)?))(pt|em|ex|mu|mm|cm|in|pc))$/)){d.Error(["BracketMustBeDimension","Bracket argument to %1 must be a dimension",l])}}this.Push(b.cell().With({isCR:true,name:l,linebreak:true}));var o=this.stack.Top();if(o.isa(b.array)){if(p&&o.arraydef.rowspacing){var m=o.arraydef.rowspacing.split(/ /);if(!o.rowspacing){o.rowspacing=this.dimen2em(m[0])}while(m.length<o.table.length){m.push(this.Em(o.rowspacing))}m[o.table.length-1]=this.Em(Math.max(0,o.rowspacing+this.dimen2em(p)));o.arraydef.rowspacing=m.join(" ")}}else{if(p){this.Push(h.mspace().With({depth:p}))}this.Push(h.mo().With({linebreak:h.LINEBREAK.NEWLINE}))}},emPerInch:7.2,dimen2em:function(p){var n=p.match(/^(-?(?:\.\d+|\d+(?:\.\d*)?))(pt|em|ex|mu|pc|in|mm|cm)/);var l=parseFloat(n[1]||"1"),o=n[2];if(o==="em"){return l}if(o==="ex"){return l*0.43}if(o==="pt"){return l/10}if(o==="pc"){return l*1.2}if(o==="in"){return l*this.emPerInch}if(o==="cm"){return l*this.emPerInch/2.54}if(o==="mm"){return l*this.emPerInch/25.4}if(o==="mu"){return l/18}return 0},Em:function(l){if(Math.abs(l)<0.0006){return"0em"}return l.toFixed(3).replace(/\.?0+$/,"")+"em"},HLine:function(m,n){if(n==null){n="solid"}var o=this.stack.Top();if(!o.isa(b.array)||o.data.length){d.Error(["Misplaced","Misplaced %1",m])}if(o.table.length==0){o.frame.push("top")}else{var l=(o.arraydef.rowlines?o.arraydef.rowlines.split(/ /):[]);while(l.length<o.table.length){l.push("none")}l[o.table.length-1]=n;o.arraydef.rowlines=l.join(" ")}},Begin:function(m){var n=this.GetArgument(m);if(n.match(/[^a-z*]/i)){d.Error(["InvalidEnv","Invalid environment name '%1'",n])}var o=this.envFindName(n);if(!o){d.Error(["UnknownEnv","Unknown environment '%1'",n])}if(++this.macroCount>d.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(!(o instanceof Array)){o=[o]}var l=b.begin().With({name:n,end:o[1],parse:this});if(o[0]&&this[o[0]]){l=this[o[0]].apply(this,[l].concat(o.slice(2)))}this.Push(l)},End:function(l){this.Push(b.end().With({name:this.GetArgument(l)}))},envFindName:function(l){return f.environment[l]},Equation:function(l,m){return m},ExtensionEnv:function(m,l){this.Extension(m.name,l,"environment")},Array:function(m,o,t,r,s,n,l,p){if(!r){r=this.GetArgument("\\begin{"+m.name+"}")}var u=("c"+r).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");r=r.replace(/[^clr]/g,"").split("").join(" ");r=r.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var q=b.array().With({arraydef:{columnalign:r,columnspacing:(s||"1em"),rowspacing:(n||"4pt")}});if(u.match(/[|:]/)){if(u.charAt(0).match(/[|:]/)){q.frame.push("left");q.frame.dashed=u.charAt(0)===":"}if(u.charAt(u.length-1).match(/[|:]/)){q.frame.push("right")}u=u.substr(1,u.length-2);q.arraydef.columnlines=u.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(o){q.open=this.convertDelimiter(o)}if(t){q.close=this.convertDelimiter(t)}if(l==="D"){q.arraydef.displaystyle=true}if(l==="S"){q.arraydef.scriptlevel=1}if(p){q.arraydef.useHeight=false}this.Push(m);return q},AlignedArray:function(l){var m=this.GetBrackets("\\begin{"+l.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),m)},setArrayAlign:function(m,l){l=this.trimSpaces(l||"");if(l==="t"){m.arraydef.align="baseline 1"}else{if(l==="b"){m.arraydef.align="baseline -1"}else{if(l==="c"){m.arraydef.align="center"}else{if(l){m.arraydef.align=l}}}}return m},convertDelimiter:function(l){if(l){l=f.delimiter[l]}if(l==null){return null}if(l instanceof Array){l=l[0]}if(l.length===4){l=String.fromCharCode(parseInt(l,16))}return l},trimSpaces:function(l){if(typeof(l)!="string"){return l}return l.replace(/^\s+|\s+$/g,"")},nextIsSpace:function(){return this.string.charAt(this.i).match(/[ \n\r\t]/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var l=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(l){this.i+=l[1].length;return l[1]}else{this.i++;return" "}},GetArgument:function(m,n){switch(this.GetNext()){case"":if(!n){d.Error(["MissingArgFor","Missing argument for %1",m])}return null;case"}":if(!n){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var l=++this.i,o=1;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"\\":this.i++;break;case"{":o++;break;case"}":if(o==0){d.Error(["ExtraClose","Extra close brace"])}if(--o==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBrace","Missing close brace"]);break}return this.string.charAt(this.i++)},GetBrackets:function(m,o){if(this.GetNext()!="["){return o}var l=++this.i,n=0;while(this.i<this.string.length){switch(this.string.charAt(this.i++)){case"{":n++;break;case"\\":this.i++;break;case"}":if(n--<=0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1","']'"])}break;case"]":if(n==0){return this.string.slice(l,this.i-1)}break}}d.Error(["MissingCloseBracket","Couldn't find closing ']' for argument to %1",m])},GetDelimiter:function(l){while(this.nextIsSpace()){this.i++}var m=this.string.charAt(this.i);if(this.i<this.string.length){this.i++;if(m=="\\"){m+=this.GetCS(l)}if(f.delimiter[m]!=null){return this.convertDelimiter(m)}}d.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",l])},GetDimen:function(m){var n;if(this.nextIsSpace()){this.i++}if(this.string.charAt(this.i)=="{"){n=this.GetArgument(m);if(n.match(/^\s*([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)\s*$/)){return n.replace(/ /g,"")}}else{n=this.string.slice(this.i);var l=n.match(/^\s*(([-+]?(\.\d+|\d+(\.\d*)?))\s*(pt|em|ex|mu|px|mm|cm|in|pc)) ?/);if(l){this.i+=l[0].length;return l[1].replace(/ /g,"")}}d.Error(["MissingDimOrUnits","Missing dimension or its units for %1",m])},GetUpTo:function(n,o){while(this.nextIsSpace()){this.i++}var m=this.i,l,q,p=0;while(this.i<this.string.length){l=this.i;q=this.string.charAt(this.i++);switch(q){case"\\":q+=this.GetCS();break;case"{":p++;break;case"}":if(p==0){d.Error(["ExtraCloseLooking","Extra close brace while looking for %1",o])}p--;break}if(p==0&&q==o){return this.string.slice(m,l)}}d.Error(["TokenNotFoundForCommand","Couldn't find %1 for %2",o,n])},ParseArg:function(l){return d.Parse(this.GetArgument(l),this.stack.env).mml()},ParseUpTo:function(l,m){return d.Parse(this.GetUpTo(l,m),this.stack.env).mml()},InternalMath:function(q,s){var p={displaystyle:false};if(s!=null){p.scriptlevel=s}if(this.stack.env.font){p.mathvariant=this.stack.env.font}if(!q.match(/\\?\$|\\\(|\\(eq)?ref\s*\{/)){return[this.InternalText(q,p)]}var o=0,l=0,r,n="";var m=[];while(o<q.length){r=q.charAt(o++);if(r==="$"){if(n==="$"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-1),{}).mml().With(p)));n="";l=o}else{if(n===""){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="$";l=o}}}else{if(r==="}"&&n==="}"){m.push(h.TeXAtom(d.Parse(q.slice(l,o),{}).mml().With(p)));n="";l=o}else{if(r==="\\"){if(n===""&&q.substr(o).match(/^(eq)?ref\s*\{/)){if(l<o-1){m.push(this.InternalText(q.slice(l,o-1),p))}n="}";l=o-1}else{r=q.charAt(o++);if(r==="("&&n===""){if(l<o-2){m.push(this.InternalText(q.slice(l,o-2),p))}n=")";l=o}else{if(r===")"&&n===")"){m.push(h.TeXAtom(d.Parse(q.slice(l,o-2),{}).mml().With(p)));n="";l=o}else{if(r==="$"&&n===""){o--;q=q.substr(0,o-1)+q.substr(o)}}}}}}}}if(n!==""){d.Error(["MathNotTerminated","Math not terminated in text box"])}if(l<q.length){m.push(this.InternalText(q.slice(l),p))}return m},InternalText:function(m,l){m=m.replace(/^\s+/,g).replace(/\s+$/,g);return h.mtext(h.chars(m)).With(l)},SubstituteArgs:function(m,l){var p="";var o="";var q;var n=0;while(n<l.length){q=l.charAt(n++);if(q==="\\"){p+=q+l.charAt(n++)}else{if(q==="#"){q=l.charAt(n++);if(q==="#"){p+=q}else{if(!q.match(/[1-9]/)||q>m.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}o=this.AddArgs(this.AddArgs(o,p),m[q-1]);p=""}}else{p+=q}}}return this.AddArgs(o,p)},AddArgs:function(m,l){if(l.match(/^[a-z]/i)&&m.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){m+=" "}if(m.length+l.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return m+l}});d.Augment({Stack:e,Parse:a,Definitions:f,Startup:k,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX 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    16. 

  16.