/*

*  /MathJax/jax/input/MathML/jax.js
*
*  Copyright (c) 2009-2018 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.
*/

(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!==“string”){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error([“ErrorParsingMathML”,“Error parsing MathML”])}}var g=j.getElementsByTagName(“parsererror”);if(g){c.Error([“ParsingError”,“Error parsing MathML: %1”,g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,“”)])}if(j.childNodes.length!==1){c.Error([“MathMLSingleElement”,“MathML must be formed by a single element”])}if(j.firstChild.nodeName.toLowerCase()===“html”){var f=j.getElementsByTagName(“h1”);if(f&&f.textContent===“XML parsing error”&&f.nextSibling){c.Error([“ParsingError”,“Error parsing MathML: %1”,String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,“”)])}}if(j.firstChild.nodeName.toLowerCase().replace(/^+:/,“”)!==“math”){c.Error([“MathMLRootElement”,“MathML must be formed by a <math> element, not %1”,“<”j.firstChild.nodeName“>”])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute(“class”)||“”);var f,g=h.nodeName.toLowerCase().replace(/^+:/,“”);var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e,e===“OP”&&!i.match(/MJX-fixedlimits/))}else{if(!(a&&a.isa&&a.isa(a.mbase))){MathJax.Hub.signal.Post([“MathML Jax - unknown node type”,g]);return a.Error(b(“UnknownNodeType”,“Unknown node type: %1”,g))}else{f=a()}}this.AddAttributes(f,h);this.CheckClass(f,f);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||“”).split(/ /);var j=[];for(var g=0,e=h.length;g<e;g++){if(h.substr(0,4)===“MJX-”){if(h===“MJX-arrow”){if(!f.notation.match(“/”a.NOTATION.UPDIAGONALARROW“/”)){f.notation+=“ ”+a.NOTATION.UPDIAGONALARROW}}else{if(h===“MJX-variant”){f.variantForm=true;if(!MathJax.Extension){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(“/extensions/TeX/AMSsymbols.js”))}}else{if(h.substr(0,11)!==“MJX-TeXAtom”){f.mathvariant=h.substr(3);if(f.mathvariant===“-tex-caligraphic-bold”||f.mathvariant===“-tex-oldstyle-bold”){if(!MathJax.Extension){MathJax.Hub.RestartAfter(MathJax.Ajax.Require(“/extensions/TeX/boldsymbol.js”))}}}}}}else{j.push(h)}}if(j.length){f=j.join(“ ”)}else{delete f}},AddAttributes:function(g,j){g.attr={};g.attrNames=[];for(var h=0,e=j.attributes.length;h<e;h++){var f=j.attributes.name;if(f==“xhref”){f=“href”}if(f.match(/:/)){continue}if(f.match(/^_moz-math-((column|row)(align|line)|font-style)$/)){continue}var k=j.attributes.value;k=this.filterAttribute(f,k);var l=(g.type===“mstyle”?a.math.prototype.defaults:g.defaults);if(k!=null){var n=k.toLowerCase();if(n===“true”||n===“false”){if(typeof(l)===“boolean”||l===a.INHERIT||g.type===“math”||g.type===“mstyle”||(l===a.AUTO&&(g.defaultDef==null||typeof(g.defaultDef)===“boolean”))){k=(n===“true”)}}if(l!=null||a.copyAttributes){g=k}else{g.attr=k}g.attrNames.push(f)}}},filterAttribute:function(e,f){return f},AddChildren:function(e,g){for(var k=0,j=g.childNodes.length;k<j;k++){var f=g.childNodes;if(f.nodeName===“#comment”){continue}if(f.nodeName===“#text”){if((e.isToken||e.isChars)&&!e.mmlSelfClosing){var o=f.nodeValue;if(e.isToken){o=o.replace(/&([a-z0-9]*);/ig,this.replaceEntity);o=this.trimSpace(o)}e.Append(a.chars(o))}else{if(f.nodeValue.match(/S/)){c.Error([“UnexpectedTextNode”,“Unexpected text node: %1”,“'”f.nodeValue“'”])}}}else{if(e.type===“annotation-xml”){e.Append(a.xml(f))}else{var h=this.MakeMML(f);e.Append(h);if(h.mmlSelfClosing&&h.data.length){e.Append.apply(e,h.data);h.data=[]}}}}if(e.type===“mrow”&&e.data.length>=2){var l=e.data,n=e.data;if(l.type===“mo”&&l.Get(“fence”)&&n.type===“mo”&&n.Get(“fence”)){if(l.data){e.open=l.data.join(“”)}if(n.data){e.close=n.data.join(“”)}}}},preProcessMath:function(f){if(f.match(/^<+:/f=f.replace(/^<(+)(:math)/i,'<$1$2 xmlns:$1=”www.w3.org/1998/Math/MathML“‘)}var e=f.match(/^(<math( ('.*?'|”.*?“|[^>])+)>)/i);if(e&&e.match(/ (?!xmlns=)+="i)){f=e[1].replace(/ (?!xmlns=)(+=(['”]).*?2)/ig,“ xmlns:$1 $1”)+f.substr(e.length)}if(f.match(/^<math[ >]/s*$/,“$2”);return“>www.w3.org/1998/Math/MathML”’)}f=f.replace(/^s*(?://)?s*$/,“$2”);return f.replace(/&([a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(//g,“ ”).replace(/^ +/,“”).replace(/ +$/,“”).replace(/ +/g,“ ”)},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity){return c.Parse.Entity}var h=f.charAt(0).toLowerCase();var e=f.match(/^(fr|scr|opf)$/);if(e){h=e}if(!c.Parse.loaded){c.Parse.loaded=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+“/”h“.js”))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:[“OriginalMathML”,“Original MathML”],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^+:/,“”)===“math”){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/(&nbsp;)+$/,“”)}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/n.*/,“”);MathJax.Hub.signal.Post([“MathML Jax - parse error”,f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,“text/xml”)},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML=“

”+e.replace(/<(+)([^>]*)/>/g,“<$1$2></$1>”)+“</div>”;var f=this.div.firstChild;this.div.innerHTML=“”;return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=;for(var g=0,e=f.length;g<e&&!j;g++){try{j=new ActiveXObject(f)}catch(h){}}return j},createParser:function(){if(window.DOMParser){this.parser=new DOMParser();return(this.parseDOM)}else{if(window.ActiveXObject){this.parser=this.createMSParser();if(!this.parser){MathJax.Localization.Try(this.parserCreationError);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)},parserCreationError:function(){alert(b(“CantCreateXMLParser”,“MathJax can't create an XML parser for MathML. Check thatnthe 'Script ActiveX controls marked safe for scripting' securitynsetting is enabled (use the Internet Options item in the Toolsnmenu, and select the Security panel, then press the Custom Levelnbutton to check this).nnMathML equations will not be able to be processed by MathJax.”))},Startup:function(){a=MathJax.ElementJax.mml;a.mspace.Augment({mmlSelfClosing:true});a.none.Augment({mmlSelfClosing:true});a.mprescripts.Augment({mmlSelfClosing:true});a.maligngroup.Augment({mmlSelfClosing:true});a.malignmark.Augment({mmlSelfClosing:true})}});c.prefilterHooks.Add(function(e){e.math=(typeof(e.math)===“string”?c.prefilterMath(e.math,e.script):c.prefilterMathML(e.math,e.script))});c.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”,bigc“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”};c.loadComplete(“jax.js”)})(MathJax.InputJax.MathML,MathJax.Hub.Browser);