/*
 *  /MathJax/jax/input/MathML/jax.js
 *  
 *  Copyright (c) 2010 Design Science, Inc.
 *
 *  Part of the MathJax library.
 *  See http://www.mathjax.org for details.
 * 
 *  Licensed under the Apache License, Version 2.0;
 *  you may not use this file except in compliance with the License.
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 */

(function(b,c){var a;b.Parse=MathJax.Object.Subclass({Init:function(d){this.Parse(d)},Parse:function(f){var g;if(typeof f!=="string"){g=f.parentNode}else{if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}f=f.replace(/^\s*(?:\/\/)?<!(--)?\[CDATA\[((.|\n)*)(\/\/)?\]\]\1>\s*$/,"$2");f=f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);g=b.ParseXML(f);if(g==null){b.Error("Error parsing MathML")}}var e=g.getElementsByTagName("parsererror")[0];if(e){b.Error("Error parsing MathML: "+e.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,""))}if(g.childNodes.length!==1){b.Error("MathML must be formed by a single element")}if(g.firstChild.nodeName.toLowerCase()==="html"){var d=g.getElementsByTagName("h1")[0];if(d&&d.textContent==="XML parsing error"&&d.nextSibling){b.Error("Error parsing MathML: "+String(d.nextSibling.nodeValue).replace(/fatal parsing error: /,""))}}if(g.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){b.Error("MathML must be formed by a <math> element, not <"+g.firstChild.nodeName+">")}this.mml=this.MakeMML(g.firstChild)},MakeMML:function(h){var l=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");if(!(a[l]&&a[l].isa&&a[l].isa(a.mbase))){return a.merror("Unknown node type: "+l)}var d=a[l](),k,j,e,n;for(k=0,j=h.attributes.length;k<j;k++){e=h.attributes[k].name;if(e=="xlink:href"){e="href"}if(e.match(/:/)){continue}n=h.attributes[k].value;if(n.toLowerCase()==="true"){n=true}else{if(n.toLowerCase()==="false"){n=false}}d[e]=n}for(k=0,j=h.childNodes.length;k<j;k++){var f=h.childNodes[k];if(f.nodeName==="#comment"){continue}if(f.nodeName==="#text"){if(d.isToken&&!d.mmlSelfClosing){var o=this.trimSpace(f.nodeValue);if(d.isa(a.mo)&&o.length===1&&this.Remap[o.charAt(0)]){o=this.Remap[o.charAt(0)]}o=o.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity);d.Append(a.chars(o))}else{if(f.nodeValue.match(/\S/)){b.Error("Unexpected text node: '"+f.nodeValue+"'")}}}else{if(d.type==="annotation-xml"){d.Append(a.xml(f))}else{var g=this.MakeMML(f);d.Append(g);if(g.mmlSelfClosing&&g.data.length){d.Append.apply(d,g.data);g.data=[]}}}}if(b.config.useMathMLspacing){d.useMMLspacing=8}return d},trimSpace:function(d){return d.replace(/^[ \t\n\r]+/,"").replace(/[ \t\n\r]+$/,"").replace(/[ \t\n\r][ \t\n\r]+/g," ")},replaceEntity:function(f,e){if(e.match(/^(lt|amp|quot)$/)){return f}if(b.Parse.Entity[e]){return b.Parse.Entity[e]}var g=e.charAt(0).toLowerCase();var d=e.match(/^[a-zA-Z](fr|scr|opf)$/);if(d){g=d[1]}if(!b.Parse.loaded[g]){b.Parse.loaded[g]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(b.entityDir+"/"+g+".js"))}return f},Remap:{"\u0027":"\u2032","\u002A":"\u2217","\u002D":"\u2212"}},{loaded:[]});b.Augment({Translate:function(d){if(!this.ParseXML){this.ParseXML=this.createParser()}var e,g;if(d.firstChild&&d.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){g=this.prefilterMathML(d.firstChild)}else{g=d.innerHTML.replace(/^\s+/,"").replace(/\s+$/,"");if(c.isMSIE){g=g.replace(/(&nbsp;)+$/,"")}else{if(c.isKonqueror){g=g.replace(/&lt;/g,"<").replace(/&gt;/g,">").replace(/&amp;/g,"&")}}g=this.prefilterMath(g,d)}try{e=b.Parse(g).mml}catch(f){if(!f.mathmlError){throw f}e=this.formatError(f,g,d)}return a(e)},prefilterMath:function(e,d){return e},prefilterMathML:function(d){return d},formatError:function(f,e,d){return a.merror(f.message.replace(/\n.*/,""))},Error:function(d){throw MathJax.Hub.Insert(Error(d),{mathmlError:true})},parseDOM:function(d){return this.parser.parseFromString(d,"text/xml")},parseMS:function(d){return(this.parser.loadXML(d)?this.parser:null)},parseDIV:function(d){this.div.innerHTML=d.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2></$1>");return this.div},parseError:function(d){return null},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){var e=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var f=0,d=e.length;f<d&&!this.parser;f++){try{this.parser=new ActiveXObject(e[f])}catch(g){}}if(!this.parser){alert("MathJax can't create an XML parser for MathML.  Check that\nthe 'Script ActiveX controls marked safe for scripting' security\nsetting is enabled (use the Internet Options item in the Tools\nmenu, and select the Security panel, then press the Custom Level\nbutton to check this).\n\nMathML equations will not be able to be processed by MathJax.");return(this.parseError)}this.parser.async=false;return(this.parseMS)}}this.div=MathJax.Hub.Insert(document.createElement("div"),{style:{visibility:"hidden",overflow:"hidden",height:"1px",position:"absolute",top:0}});if(!document.body.firstChild){document.body.appendChild(this.div)}else{document.body.insertBefore(this.div,document.body.firstChild)}return(this.parseDIV)},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClossing:true})}});b.Parse.Entity={ApplyFunction:"\u2061",Backslash:"\u2216",Because:"\u2235",Breve:"\u02D8",Cap:"\u22D2",CenterDot:"\u00B7",CircleDot:"\u2299",CircleMinus:"\u2296",CirclePlus:"\u2295",CircleTimes:"\u2297",Congruent:"\u2261",ContourIntegral:"\u222E",Coproduct:"\u2210",Cross:"\u2A2F",Cup:"\u22D3",CupCap:"\u224D",Dagger:"\u2021",Del:"\u2207",Delta:"\u0394",Diamond:"\u22C4",DifferentialD:"\u2146",DotEqual:"\u2250",DoubleDot:"\u00A8",DoubleRightTee:"\u22A8",DoubleVerticalBar:"\u2225",DownArrow:"\u2193",DownLeftVector:"\u21BD",DownRightVector:"\u21C1",DownTee:"\u22A4",Downarrow:"\u21D3",Element:"\u2208",EqualTilde:"\u2242",Equilibrium:"\u21CC",Exists:"\u2203",ExponentialE:"\u2147",FilledVerySmallSquare:"\u25AA",ForAll:"\u2200",Gamma:"\u0393",Gg:"\u22D9",GreaterEqual:"\u2265",GreaterEqualLess:"\u22DB",GreaterFullEqual:"\u2267",GreaterLess:"\u2277",GreaterSlantEqual:"\u2A7E",GreaterTilde:"\u2273",Hacek:"\u02C7",Hat:"\u005E",HumpDownHump:"\u224E",HumpEqual:"\u224F",Im:"\u2111",ImaginaryI:"\u2148",Integral:"\u222B",Intersection:"\u22C2",InvisibleComma:"\u2063",InvisibleTimes:"\u2062",Lambda:"\u039B",Larr:"\u219E",LeftAngleBracket:"\u27E8",LeftArrow:"\u2190",LeftArrowRightArrow:"\u21C6",LeftCeiling:"\u2308",LeftDownVector:"\u21C3",LeftFloor:"\u230A",LeftRightArrow:"\u2194",LeftTee:"\u22A3",LeftTriangle:"\u22B2",LeftTriangleEqual:"\u22B4",LeftUpVector:"\u21BF",LeftVector:"\u21BC",Leftarrow:"\u21D0",Leftrightarrow:"\u21D4",LessEqualGreater:"\u22DA",LessFullEqual:"\u2266",LessGreater:"\u2276",LessSlantEqual:"\u2A7D",LessTilde:"\u2272",Ll:"\u22D8",Lleftarrow:"\u21DA",LongLeftArrow:"\u27F5",LongLeftRightArrow:"\u27F7",LongRightArrow:"\u27F6",Longleftarrow:"\u27F8",Longleftrightarrow:"\u27FA",Longrightarrow:"\u27F9",Lsh:"\u21B0",MinusPlus:"\u2213",NestedGreaterGreater:"\u226B",NestedLessLess:"\u226A",NotDoubleVerticalBar:"\u2226",NotElement:"\u2209",NotEqual:"\u2260",NotExists:"\u2204",NotGreater:"\u226F",NotGreaterEqual:"\u2271",NotLeftTriangle:"\u22EA",NotLeftTriangleEqual:"\u22EC",NotLess:"\u226E",NotLessEqual:"\u2270",NotPrecedes:"\u2280",NotPrecedesSlantEqual:"\u22E0",NotRightTriangle:"\u22EB",NotRightTriangleEqual:"\u22ED",NotSubsetEqual:"\u2288",NotSucceeds:"\u2281",NotSucceedsSlantEqual:"\u22E1",NotSupersetEqual:"\u2289",NotTilde:"\u2241",NotVerticalBar:"\u2224",Omega:"\u03A9",OverBar:"\u203E",OverBrace:"\u23DE",PartialD:"\u2202",Phi:"\u03A6",Pi:"\u03A0",PlusMinus:"\u00B1",Precedes:"\u227A",PrecedesEqual:"\u2AAF",PrecedesSlantEqual:"\u227C",PrecedesTilde:"\u227E",Product:"\u220F",Proportional:"\u221D",Psi:"\u03A8",Rarr:"\u21A0",Re:"\u211C",ReverseEquilibrium:"\u21CB",RightAngleBracket:"\u27E9",RightArrow:"\u2192",RightArrowLeftArrow:"\u21C4",RightCeiling:"\u2309",RightDownVector:"\u21C2",RightFloor:"\u230B",RightTee:"\u22A2",RightTeeArrow:"\u21A6",RightTriangle:"\u22B3",RightTriangleEqual:"\u22B5",RightUpVector:"\u21BE",RightVector:"\u21C0",Rightarrow:"\u21D2",Rrightarrow:"\u21DB",Rsh:"\u21B1",Sigma:"\u03A3",SmallCircle:"\u2218",Sqrt:"\u221A",Square:"\u25A1",SquareIntersection:"\u2293",SquareSubset:"\u228F",SquareSubsetEqual:"\u2291",SquareSuperset:"\u2290",SquareSupersetEqual:"\u2292",SquareUnion:"\u2294",Star:"\u22C6",Subset:"\u22D0",SubsetEqual:"\u2286",Succeeds:"\u227B",SucceedsEqual:"\u2AB0",SucceedsSlantEqual:"\u227D",SucceedsTilde:"\u227F",SuchThat:"\u220B",Sum:"\u2211",Superset:"\u2283",SupersetEqual:"\u2287",Supset:"\u22D1",Therefore:"\u2234",Theta:"\u0398",Tilde:"\u223C",TildeEqual:"\u2243",TildeFullEqual:"\u2245",TildeTilde:"\u2248",UnderBar:"\u005F",UnderBrace:"\u23DF",Union:"\u22C3",UnionPlus:"\u228E",UpArrow:"\u2191",UpDownArrow:"\u2195",UpTee:"\u22A5",Uparrow:"\u21D1",Updownarrow:"\u21D5",Upsilon:"\u03A5",Vdash:"\u22A9",Vee:"\u22C1",VerticalBar:"\u2223",VerticalTilde:"\u2240",Vvdash:"\u22AA",Wedge:"\u22C0",Xi:"\u039E",acute:"\u00B4",aleph:"\u2135",alpha:"\u03B1",amalg:"\u2A3F",and:"\u2227",ang:"\u2220",angmsd:"\u2221",angsph:"\u2222",ape:"\u224A",backprime:"\u2035",backsim:"\u223D",backsimeq:"\u22CD",beta:"\u03B2",beth:"\u2136",between:"\u226C",bigcirc:"\u25EF",bigodot:"\u2A00",bigoplus:"\u2A01",bigotimes:"\u2A02",bigsqcup:"\u2A06",bigstar:"\u2605",bigtriangledown:"\u25BD",bigtriangleup:"\u25B3",biguplus:"\u2A04",blacklozenge:"\u29EB",blacktriangle:"\u25B4",blacktriangledown:"\u25BE",blacktriangleleft:"\u25C2",bowtie:"\u22C8",boxdl:"\u2510",boxdr:"\u250C",boxminus:"\u229F",boxplus:"\u229E",boxtimes:"\u22A0",boxul:"\u2518",boxur:"\u2514",bsol:"\u005C",bull:"\u2022",cap:"\u2229",check:"\u2713",chi:"\u03C7",circ:"\u02C6",circeq:"\u2257",circlearrowleft:"\u21BA",circlearrowright:"\u21BB",circledR:"\u00AE",circledS:"\u24C8",circledast:"\u229B",circledcirc:"\u229A",circleddash:"\u229D",clubs:"\u2663",colon:"\u003A",comp:"\u2201",ctdot:"\u22EF",cuepr:"\u22DE",cuesc:"\u22DF",cularr:"\u21B6",cup:"\u222A",curarr:"\u21B7",curlyvee:"\u22CE",curlywedge:"\u22CF",dagger:"\u2020",daleth:"\u2138",ddarr:"\u21CA",deg:"\u00B0",delta:"\u03B4",digamma:"\u03DD",div:"\u00F7",divideontimes:"\u22C7",dot:"\u02D9",doteqdot:"\u2251",dotplus:"\u2214",dotsquare:"\u22A1",dtdot:"\u22F1",ecir:"\u2256",efDot:"\u2252",egs:"\u2A96",ell:"\u2113",els:"\u2A95",empty:"\u2205",epsi:"\u03B5",epsiv:"\u03F5",erDot:"\u2253",eta:"\u03B7",eth:"\u00F0",flat:"\u266D",fork:"\u22D4",frown:"\u2322",gEl:"\u2A8C",gamma:"\u03B3",gap:"\u2A86",gimel:"\u2137",gnE:"\u2269",gnap:"\u2A8A",gne:"\u2A88",gnsim:"\u22E7",gt:"\u003E",gtdot:"\u22D7",harrw:"\u21AD",hbar:"\u210F",hellip:"\u2026",hookleftarrow:"\u21A9",hookrightarrow:"\u21AA",imath:"\u0131",infin:"\u221E",intcal:"\u22BA",iota:"\u03B9",jmath:"\u0237",kappa:"\u03BA",kappav:"\u03F0",lEg:"\u2A8B",lambda:"\u03BB",lap:"\u2A85",larrlp:"\u21AB",larrtl:"\u21A2",lbrace:"\u007B",lbrack:"\u005B",le:"\u2264",leftleftarrows:"\u21C7",leftthreetimes:"\u22CB",lessdot:"\u22D6",lmoust:"\u23B0",lnE:"\u2268",lnap:"\u2A89",lne:"\u2A87",lnsim:"\u22E6",longmapsto:"\u27FC",looparrowright:"\u21AC",lowast:"\u2217",loz:"\u25CA",lt:"\u003C",ltimes:"\u22C9",ltri:"\u25C3",macr:"\u00AF",malt:"\u2720",mho:"\u2127",mu:"\u03BC",multimap:"\u22B8",nLeftarrow:"\u21CD",nLeftrightarrow:"\u21CE",nRightarrow:"\u21CF",nVDash:"\u22AF",nVdash:"\u22AE",natur:"\u266E",nearr:"\u2197",nharr:"\u21AE",nlarr:"\u219A",not:"\u00AC",nrarr:"\u219B",nu:"\u03BD",nvDash:"\u22AD",nvdash:"\u22AC",nwarr:"\u2196",omega:"\u03C9",omicron:"\u03BF",or:"\u2228",osol:"\u2298",period:"\u002E",phi:"\u03C6",phiv:"\u03D5",pi:"\u03C0",piv:"\u03D6",prap:"\u2AB7",precnapprox:"\u2AB9",precneqq:"\u2AB5",precnsim:"\u22E8",prime:"\u2032",psi:"\u03C8",rarrtl:"\u21A3",rbrace:"\u007D",rbrack:"\u005D",rho:"\u03C1",rhov:"\u03F1",rightrightarrows:"\u21C9",rightthreetimes:"\u22CC",ring:"\u02DA",rmoust:"\u23B1",rtimes:"\u22CA",rtri:"\u25B9",scap:"\u2AB8",scnE:"\u2AB6",scnap:"\u2ABA",scnsim:"\u22E9",sdot:"\u22C5",searr:"\u2198",sect:"\u00A7",sharp:"\u266F",sigma:"\u03C3",sigmav:"\u03C2",simne:"\u2246",smile:"\u2323",spades:"\u2660",sub:"\u2282",subE:"\u2AC5",subnE:"\u2ACB",subne:"\u228A",supE:"\u2AC6",supnE:"\u2ACC",supne:"\u228B",swarr:"\u2199",tau:"\u03C4",theta:"\u03B8",thetav:"\u03D1",tilde:"\u02DC",times:"\u00D7",triangle:"\u25B5",triangleq:"\u225C",upsi:"\u03C5",upuparrows:"\u21C8",veebar:"\u22BB",vellip:"\u22EE",weierp:"\u2118",xi:"\u03BE",yen:"\u00A5",zeta:"\u03B6",zigrarr:"\u21DD"};b.loadComplete("jax.js")})(MathJax.InputJax.MathML,MathJax.Hub.Browser);