# HG changeset patch # User gibus # Date 1394467269 -3600 # Node ID 0dad543d4ed03d57149af2ae032edd7cfe3f93aa # Parent f4661cf8fdd9de3b5c1c0880d34810e33fc1c109 In ASCIIMathML just skip onload translate from Latex. diff -r f4661cf8fdd9 -r 0dad543d4ed0 src/cm/media/js/lib/asciimathtml/ASCIIMathML.js --- a/src/cm/media/js/lib/asciimathtml/ASCIIMathML.js Mon Mar 10 16:48:48 2014 +0100 +++ b/src/cm/media/js/lib/asciimathtml/ASCIIMathML.js Mon Mar 10 17:01:09 2014 +0100 @@ -42,9 +42,9 @@ var checkForMathML = true; // check if browser can display MathML var notifyIfNoMathML = true; // display note at top if no MathML capability var alertIfNoMathML = false; // show alert box if no MathML capability -var translateOnLoad = false; // set to false to do call translators from js -var translateLaTeX = true; // false to preserve $..$, $$..$$ -var translateLaTeXformatting = true; // false to preserve \emph,\begin{},\end{} +var translateOnLoad = true; // set to false to do call translators from js +var translateLaTeX = false; // false to preserve $..$, $$..$$ +var translateLaTeXformatting = false; // false to preserve \emph,\begin{},\end{} var translateASCIIMath = true; // false to preserve `..` var translateASCIIsvg = true; // false to preserve agraph.., \begin{graph}.. var avoidinnerHTML = false; // set true if assigning to innerHTML gives error diff -r f4661cf8fdd9 -r 0dad543d4ed0 src/cm/media/js/lib/asciimathtml/ASCIIMathML.min.js --- a/src/cm/media/js/lib/asciimathtml/ASCIIMathML.min.js Mon Mar 10 16:48:48 2014 +0100 +++ b/src/cm/media/js/lib/asciimathtml/ASCIIMathML.min.js Mon Mar 10 17:01:09 2014 +0100 @@ -1,1 +1,1 @@ -var mathcolor="blue";var mathfontsize="1em";var mathfontfamily="serif";var automathrecognize=false;var checkForMathML=true;var notifyIfNoMathML=true;var alertIfNoMathML=false;var translateOnLoad=false;var translateLaTeX=true;var translateLaTeXformatting=true;var translateASCIIMath=true;var translateASCIIsvg=true;var avoidinnerHTML=false;var displaystyle=true;var showasciiformulaonhover=true;var decimalsign=".";var AMdelimiter1="`",AMescape1="\\\\`";var AMdocumentId="wikitext";var checkforprocessasciimathinmoodle=false;var dsvglocation="";var isIE=document.createElementNS==null;if(document.getElementById==null){alert("This webpage requires a recent browser such as\nMozilla/Netscape 7+ or Internet Explorer 6+MathPlayer");}function AMcreateElementXHTML(f){if(isIE){return document.createElement(f);}else{return document.createElementNS("http://www.w3.org/1999/xhtml",f);}}function AMnoMathMLNote(){var g=AMcreateElementXHTML("h3");g.setAttribute("align","center");g.appendChild(AMcreateElementXHTML("p"));g.appendChild(document.createTextNode("To view the "));var f=AMcreateElementXHTML("a");f.appendChild(document.createTextNode("ASCIIMathML"));f.setAttribute("href","http://www.chapman.edu/~jipsen/asciimath.html");g.appendChild(f);g.appendChild(document.createTextNode(" notation use Internet Explorer 6+"));f=AMcreateElementXHTML("a");f.appendChild(document.createTextNode("MathPlayer"));f.setAttribute("href","http://www.dessci.com/en/products/mathplayer/download.htm");g.appendChild(f);g.appendChild(document.createTextNode(" or Netscape/Mozilla/Firefox"));g.appendChild(AMcreateElementXHTML("p"));return g;}function AMisMathMLavailable(){if(navigator.appName.slice(0,8)=="Netscape"){if(navigator.appVersion.slice(0,1)>="5"){return null;}else{return AMnoMathMLNote();}}else{if(navigator.appName.slice(0,9)=="Microsoft"){try{var g=new ActiveXObject("MathPlayer.Factory.1");return null;}catch(f){return AMnoMathMLNote();}}else{return AMnoMathMLNote();}}}var AMcal=[61237,8492,61238,61239,8496,8497,61240,8459,8464,61241,61242,8466,8499,61243,61244,61245,61246,8475,61247,61248,61249,61250,61251,61252,61253,61254];var AMfrk=[61277,61278,8493,61279,61280,61281,61282,8460,8465,61283,61284,61285,61286,61287,61288,61289,61290,8476,61291,61292,61293,61294,61295,61296,61297,8488];var AMbbb=[61324,61325,8450,61326,61327,61328,61329,8461,61330,61331,61332,61333,61334,8469,61335,8473,8474,8477,61336,61337,61338,61339,61340,61341,61342,8484];var CONST=0,UNARY=1,BINARY=2,INFIX=3,LEFTBRACKET=4,RIGHTBRACKET=5,SPACE=6,UNDEROVER=7,DEFINITION=8,LEFTRIGHT=9,TEXT=10;var AMsqrt={input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:UNARY},AMroot={input:"root",tag:"mroot",output:"root",tex:null,ttype:BINARY},AMfrac={input:"frac",tag:"mfrac",output:"/",tex:null,ttype:BINARY},AMdiv={input:"/",tag:"mfrac",output:"/",tex:null,ttype:INFIX},AMover={input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:BINARY},AMsub={input:"_",tag:"msub",output:"_",tex:null,ttype:INFIX},AMsup={input:"^",tag:"msup",output:"^",tex:null,ttype:INFIX},AMtext={input:"text",tag:"mtext",output:"text",tex:null,ttype:TEXT},AMmbox={input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:TEXT},AMquote={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:TEXT};var AMsymbols=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:CONST},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:CONST},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:CONST},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:CONST},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:CONST},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:CONST},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:CONST},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:CONST},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:CONST},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:CONST},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:CONST},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:CONST},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:CONST},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:CONST},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:CONST},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:CONST},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:CONST},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:CONST},{input:"phi",tag:"mi",output:"\u03C6",tex:null,ttype:CONST},{input:"varphi",tag:"mi",output:"\u03D5",tex:null,ttype:CONST},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:CONST},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:CONST},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:CONST},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:CONST},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:CONST},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:CONST},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:CONST},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:CONST},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:CONST},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:CONST},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:CONST},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:CONST},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:CONST},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:CONST},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:CONST},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:CONST},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:CONST},{input:"**",tag:"mo",output:"\u22C6",tex:"star",ttype:CONST},{input:"//",tag:"mo",output:"/",tex:null,ttype:CONST},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:CONST},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:CONST},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:CONST},{input:"-:",tag:"mo",output:"\u00F7",tex:"divide",ttype:CONST},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:CONST},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:CONST},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:CONST},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:CONST},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:UNDEROVER},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:UNDEROVER},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:CONST},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:UNDEROVER},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:CONST},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:UNDEROVER},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:CONST},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:UNDEROVER},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:CONST},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:UNDEROVER},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:CONST},{input:":=",tag:"mo",output:":=",tex:null,ttype:CONST},{input:"lt",tag:"mo",output:"<",tex:null,ttype:CONST},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:CONST},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:CONST},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:CONST},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:CONST},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:CONST},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:CONST},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:CONST},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:CONST},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:CONST},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:CONST},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:CONST},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:CONST},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:CONST},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:CONST},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:CONST},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:CONST},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:CONST},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:CONST},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:CONST},{input:"and",tag:"mtext",output:"and",tex:null,ttype:SPACE},{input:"or",tag:"mtext",output:"or",tex:null,ttype:SPACE},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:CONST},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:CONST},{input:"if",tag:"mo",output:"if",tex:null,ttype:SPACE},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:CONST},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:CONST},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:CONST},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:CONST},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:CONST},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:CONST},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:CONST},{input:"(",tag:"mo",output:"(",tex:null,ttype:LEFTBRACKET},{input:")",tag:"mo",output:")",tex:null,ttype:RIGHTBRACKET},{input:"[",tag:"mo",output:"[",tex:null,ttype:LEFTBRACKET},{input:"]",tag:"mo",output:"]",tex:null,ttype:RIGHTBRACKET},{input:"{",tag:"mo",output:"{",tex:null,ttype:LEFTBRACKET},{input:"}",tag:"mo",output:"}",tex:null,ttype:RIGHTBRACKET},{input:"|",tag:"mo",output:"|",tex:null,ttype:LEFTRIGHT},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:LEFTBRACKET},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:RIGHTBRACKET},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:LEFTBRACKET},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:RIGHTBRACKET},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:LEFTBRACKET,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:RIGHTBRACKET,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:CONST},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:DEFINITION},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:DEFINITION},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:DEFINITION},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:DEFINITION},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:CONST},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:CONST},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:CONST},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:CONST},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:CONST},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:CONST},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:CONST},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:CONST},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:CONST},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:CONST},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:CONST},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:CONST},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:CONST},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:CONST},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:CONST},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:CONST},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:CONST},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:CONST},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:CONST},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:CONST},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:CONST},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:CONST},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:CONST},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:CONST},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:CONST},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:CONST},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:CONST},{input:"f",tag:"mi",output:"f",tex:null,ttype:UNARY,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:UNARY,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:UNDEROVER},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:UNDEROVER},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:UNARY,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:UNARY,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:UNARY,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:UNARY,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:UNARY,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:UNARY,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:UNARY,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:UNARY,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:UNARY,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:UNARY,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:UNARY,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:UNARY,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:CONST},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:CONST},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:UNARY,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:UNARY,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:CONST},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:CONST},{input:"min",tag:"mo",output:"min",tex:null,ttype:UNDEROVER},{input:"max",tag:"mo",output:"max",tex:null,ttype:UNDEROVER},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:CONST},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:CONST},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:CONST},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:CONST},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:CONST},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:CONST},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:CONST},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:CONST},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:CONST},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:CONST},AMsqrt,AMroot,AMfrac,AMdiv,AMover,AMsub,AMsup,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:UNARY,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:UNARY,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:UNARY,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:UNARY,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:UNARY,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:UNARY,acc:true},AMtext,AMmbox,AMquote,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:UNARY},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:UNARY},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:UNARY},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:UNARY},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:UNARY,codes:AMbbb},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:UNARY,codes:AMbbb},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:UNARY,codes:AMcal},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:UNARY,codes:AMcal},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:UNARY},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:UNARY},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:UNARY,codes:AMfrk},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:UNARY,codes:AMfrk}];function compareNames(g,f){if(g.input>f.input){return 1;}else{return -1;}}var AMnames=[];function AMinitSymbols(){var g=[],f;for(f=0;f>1;if(g[f]=AMnames[f];}AMpreviousSymbol=AMcurrentSymbol;if(m!=""){AMcurrentSymbol=AMsymbols[l].ttype;return AMsymbols[l];}AMcurrentSymbol=CONST;f=1;v=q.slice(0,1);var r=true;while("0"<=v&&v<="9"&&f<=q.length){v=q.slice(f,f+1);f++;}if(v==decimalsign){v=q.slice(f,f+1);if("0"<=v&&v<="9"){r=false;f++;while("0"<=v&&v<="9"&&f<=q.length){v=q.slice(f,f+1);f++;}}}if((r&&f>1)||f>2){v=q.slice(0,f-1);s="mn";}else{f=2;v=q.slice(0,1);s=(("A">v||v>"Z")&&("a">v||v>"z")?"mo":"mi");}if(v=="-"&&AMpreviousSymbol==INFIX){AMcurrentSymbol=INFIX;return{input:v,tag:s,output:v,ttype:UNARY,func:true};}return{input:v,tag:s,output:v,ttype:CONST};}function AMremoveBrackets(g){var f;if(g.nodeName=="mrow"){f=g.firstChild.firstChild.nodeValue;if(f=="("||f=="["||f=="{"){g.removeChild(g.firstChild);}}if(g.nodeName=="mrow"){f=g.lastChild.firstChild.nodeValue;if(f==")"||f=="]"||f=="}"){g.removeChild(g.lastChild);}}}var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol;function AMparseSexpr(o){var h,g,s,l,r,m=document.createDocumentFragment();o=AMremoveCharsAndBlanks(o,0);h=AMgetSymbol(o);if(h==null||h.ttype==RIGHTBRACKET&&AMnestingDepth>0){return[null,o];}if(h.ttype==DEFINITION){o=h.output+AMremoveCharsAndBlanks(o,h.input.length);h=AMgetSymbol(o);}switch(h.ttype){case UNDEROVER:case CONST:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];case LEFTBRACKET:AMnestingDepth++;o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseExpr(o,true);AMnestingDepth--;if(typeof h.invisible=="boolean"&&h.invisible){g=AMcreateMmlNode("mrow",s[0]);}else{g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);g.appendChild(s[0]);}return[g,s[1]];case TEXT:if(h!=AMquote){o=AMremoveCharsAndBlanks(o,h.input.length);}if(o.charAt(0)=="{"){l=o.indexOf("}");}else{if(o.charAt(0)=="("){l=o.indexOf(")");}else{if(o.charAt(0)=="["){l=o.indexOf("]");}else{if(h==AMquote){l=o.slice(1).indexOf('"')+1;}else{l=0;}}}}if(l==-1){l=o.length;}r=o.slice(1,l);if(r.charAt(0)==" "){g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);}m.appendChild(AMcreateMmlNode(h.tag,document.createTextNode(r)));if(r.charAt(r.length-1)==" "){g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);}o=AMremoveCharsAndBlanks(o,l+1);return[AMcreateMmlNode("mrow",m),o];case UNARY:o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseSexpr(o);if(s[0]==null){return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}if(typeof h.func=="boolean"&&h.func){r=o.charAt(0);if(r=="^"||r=="_"||r=="/"||r=="|"||r==","){return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}else{g=AMcreateMmlNode("mrow",AMcreateMmlNode(h.tag,document.createTextNode(h.output)));g.appendChild(s[0]);return[g,s[1]];}}AMremoveBrackets(s[0]);if(h.input=="sqrt"){return[AMcreateMmlNode(h.tag,s[0]),s[1]];}else{if(typeof h.acc=="boolean"&&h.acc){g=AMcreateMmlNode(h.tag,s[0]);g.appendChild(AMcreateMmlNode("mo",document.createTextNode(h.output)));return[g,s[1]];}else{if(!isIE&&typeof h.codes!="undefined"){for(l=0;l64&&r.charCodeAt(k)<91){q=q+String.fromCharCode(h.codes[r.charCodeAt(k)-65]);}else{q=q+r.charAt(k);}}if(s[0].nodeName=="mi"){s[0]=AMcreateElementMathML("mo").appendChild(document.createTextNode(q));}else{s[0].replaceChild(AMcreateElementMathML("mo").appendChild(document.createTextNode(q)),s[0].childNodes[l]);}}}}g=AMcreateMmlNode(h.tag,s[0]);g.setAttribute(h.atname,h.atval);return[g,s[1]];}}case BINARY:o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseSexpr(o);if(s[0]==null){return[AMcreateMmlNode("mo",document.createTextNode(h.input)),o];}AMremoveBrackets(s[0]);var f=AMparseSexpr(s[1]);if(f[0]==null){return[AMcreateMmlNode("mo",document.createTextNode(h.input)),o];}AMremoveBrackets(f[0]);if(h.input=="root"||h.input=="stackrel"){m.appendChild(f[0]);}m.appendChild(s[0]);if(h.input=="frac"){m.appendChild(f[0]);}return[AMcreateMmlNode(h.tag,m),f[1]];case INFIX:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode("mo",document.createTextNode(h.output)),o];case SPACE:o=AMremoveCharsAndBlanks(o,h.input.length);g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);m.appendChild(AMcreateMmlNode(h.tag,document.createTextNode(h.output)));g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);return[AMcreateMmlNode("mrow",m),o];case LEFTRIGHT:AMnestingDepth++;o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseExpr(o,false);AMnestingDepth--;var r="";if(s[0].lastChild!=null){r=s[0].lastChild.firstChild.nodeValue;}if(r=="|"){g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);g.appendChild(s[0]);return[g,s[1]];}else{g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);return[g,o];}default:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}}function AMparseIexpr(m){var k,o,l,j,f,h;m=AMremoveCharsAndBlanks(m,0);o=AMgetSymbol(m);f=AMparseSexpr(m);j=f[0];m=f[1];k=AMgetSymbol(m);if(k.ttype==INFIX&&k.input!="/"){m=AMremoveCharsAndBlanks(m,k.input.length);f=AMparseSexpr(m);if(f[0]==null){f[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));}else{AMremoveBrackets(f[0]);}m=f[1];if(k.input=="_"){l=AMgetSymbol(m);h=(o.ttype==UNDEROVER);if(l.input=="^"){m=AMremoveCharsAndBlanks(m,l.input.length);var g=AMparseSexpr(m);AMremoveBrackets(g[0]);m=g[1];j=AMcreateMmlNode((h?"munderover":"msubsup"),j);j.appendChild(f[0]);j.appendChild(g[0]);j=AMcreateMmlNode("mrow",j);}else{j=AMcreateMmlNode((h?"munder":"msub"),j);j.appendChild(f[0]);}}else{j=AMcreateMmlNode(k.tag,j);j.appendChild(f[0]);}}return[j,m];}function AMparseExpr(v,s){var B,w,o,F,J=[],q=document.createDocumentFragment();do{v=AMremoveCharsAndBlanks(v,0);o=AMparseIexpr(v);w=o[0];v=o[1];B=AMgetSymbol(v);if(B.ttype==INFIX&&B.input=="/"){v=AMremoveCharsAndBlanks(v,B.input.length);o=AMparseIexpr(v);if(o[0]==null){o[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));}else{AMremoveBrackets(o[0]);}v=o[1];AMremoveBrackets(w);w=AMcreateMmlNode(B.tag,w);w.appendChild(o[0]);q.appendChild(w);B=AMgetSymbol(v);}else{if(w!=undefined){q.appendChild(w);}}}while((B.ttype!=RIGHTBRACKET&&(B.ttype!=LEFTRIGHT||s)||AMnestingDepth==0)&&B!=null&&B.output!="");if(B.ttype==RIGHTBRACKET||B.ttype==LEFTRIGHT){var G=q.childNodes.length;if(G>0&&q.childNodes[G-1].nodeName=="mrow"&&G>1&&q.childNodes[G-2].nodeName=="mo"&&q.childNodes[G-2].firstChild.nodeValue==","){var I=q.childNodes[G-1].lastChild.firstChild.nodeValue;if(I==")"||I=="]"){var g=q.childNodes[G-1].firstChild.firstChild.nodeValue;if(g=="("&&I==")"&&B.output!="}"||g=="["&&I=="]"){var h=[];var D=true;var z=q.childNodes.length;for(F=0;D&&F1){D=h[F].length==h[F-2].length;}}if(D){var l,f,r,A,H=document.createDocumentFragment();for(F=0;F2){q.removeChild(q.firstChild);q.removeChild(q.firstChild);}H.appendChild(AMcreateMmlNode("mtr",l));}w=AMcreateMmlNode("mtable",H);if(typeof B.invisible=="boolean"&&B.invisible){w.setAttribute("columnalign","left");}q.replaceChild(w,q.firstChild);}}}}v=AMremoveCharsAndBlanks(v,B.input.length);if(typeof B.invisible!="boolean"||!B.invisible){w=AMcreateMmlNode("mo",document.createTextNode(B.output));q.appendChild(w);}}return[q,v];}function AMparseMath(j){var f,h=AMcreateElementMathML("mstyle");if(mathcolor!=""){h.setAttribute("mathcolor",mathcolor);}if(displaystyle){h.setAttribute("displaystyle","true");}if(mathfontfamily!=""){h.setAttribute("fontfamily",mathfontfamily);}AMnestingDepth=0;h.appendChild(AMparseExpr(j.replace(/^\s+/g,""),false)[0]);h=AMcreateMmlNode("math",h);if(showasciiformulaonhover){h.setAttribute("title",j.replace(/\s+/g," "));}var g=AMcreateElementXHTML("span");g.style.fontSize=mathfontsize;if(mathfontfamily!=""){g.style.fontFamily=mathfontfamily;}g.appendChild(h);return g;}function AMstrarr2docFrag(f,k){var o=document.createDocumentFragment();var m=false;for(var l=0;l,\\|!:;'~]|\\.(?!(?:\x20|$))|"+q+s+f;var v=new RegExp("(^|\\s)((("+k+")\\s?)(("+k+j+")\\s?)+)([,.?]?(?=\\s|$))","g");r=r.replace(v," `$2`$7");var m=r.split(AMdelimiter1);var o=new RegExp("(^|\\s)([b-zB-HJ-Z+*<>]|"+h+q+f+")(\\s|\\n|$)","g");var l=new RegExp("(^|\\s)([a-z]|"+h+q+f+")([,.])","g");for(i=0;i1||q){if(checkForMathML){checkForMathML=false;var h=AMisMathMLavailable();AMnoMathML=h!=null;if(AMnoMathML&¬ifyIfNoMathML){if(alertIfNoMathML){alert("To view the ASCIIMathML notation use Internet Explorer 6 +\nMathPlayer (free from www.dessci.com)\n or Firefox/Mozilla/Netscape");}else{AMbody.insertBefore(h,AMbody.childNodes[0]);}}}if(!AMnoMathML){f=AMstrarr2docFrag(k,g.nodeType==8);var l=f.childNodes.length;g.parentNode.replaceChild(f,g);return l-1;}else{return 0;}}}}else{return 0;}}else{if(g.nodeName!="math"){for(j=0;j="5"){return null;}else{return LMnoMathMLNote();}}else{if(navigator.appName.slice(0,9)=="Microsoft"){try{var g=new ActiveXObject("MathPlayer.Factory.1");return null;}catch(f){return LMnoMathMLNote();}}else{return LMnoMathMLNote();}}}var LMcal=[61237,8492,61238,61239,8496,8497,61240,8459,8464,61241,61242,8466,8499,61243,61244,61245,61246,8475,61247,61248,61249,61250,61251,61252,61253,61254];var LMfrk=[61277,61278,8493,61279,61280,61281,61282,8460,8465,61283,61284,61285,61286,61287,61288,61289,61290,8476,61291,61292,61293,61294,61295,61296,61297,8488];var LMbbb=[61324,61325,8450,61326,61327,61328,61329,8461,61330,61331,61332,61333,61334,8469,61335,8473,8474,8477,61336,61337,61338,61339,61340,61341,61342,8484];var BIG=11,LONG=12,STRETCHY=13,MATRIX=14;var LMsqrt={input:"\\sqrt",tag:"msqrt",output:"sqrt",ttype:UNARY},LMroot={input:"\\root",tag:"mroot",output:"root",ttype:BINARY},LMfrac={input:"\\frac",tag:"mfrac",output:"/",ttype:BINARY},LMover={input:"\\stackrel",tag:"mover",output:"stackrel",ttype:BINARY},LMatop={input:"\\atop",tag:"mfrac",output:"",ttype:INFIX},LMchoose={input:"\\choose",tag:"mfrac",output:"",ttype:INFIX},LMsub={input:"_",tag:"msub",output:"_",ttype:INFIX},LMsup={input:"^",tag:"msup",output:"^",ttype:INFIX},LMtext={input:"\\mathrm",tag:"mtext",output:"text",ttype:TEXT},LMmbox={input:"\\mbox",tag:"mtext",output:"mbox",ttype:TEXT};var LMsymbols=[{input:"\\alpha",tag:"mi",output:"\u03B1",ttype:CONST},{input:"\\beta",tag:"mi",output:"\u03B2",ttype:CONST},{input:"\\gamma",tag:"mi",output:"\u03B3",ttype:CONST},{input:"\\delta",tag:"mi",output:"\u03B4",ttype:CONST},{input:"\\epsilon",tag:"mi",output:"\u03B5",ttype:CONST},{input:"\\varepsilon",tag:"mi",output:"\u025B",ttype:CONST},{input:"\\zeta",tag:"mi",output:"\u03B6",ttype:CONST},{input:"\\eta",tag:"mi",output:"\u03B7",ttype:CONST},{input:"\\theta",tag:"mi",output:"\u03B8",ttype:CONST},{input:"\\vartheta",tag:"mi",output:"\u03D1",ttype:CONST},{input:"\\iota",tag:"mi",output:"\u03B9",ttype:CONST},{input:"\\kappa",tag:"mi",output:"\u03BA",ttype:CONST},{input:"\\lambda",tag:"mi",output:"\u03BB",ttype:CONST},{input:"\\mu",tag:"mi",output:"\u03BC",ttype:CONST},{input:"\\nu",tag:"mi",output:"\u03BD",ttype:CONST},{input:"\\xi",tag:"mi",output:"\u03BE",ttype:CONST},{input:"\\pi",tag:"mi",output:"\u03C0",ttype:CONST},{input:"\\varpi",tag:"mi",output:"\u03D6",ttype:CONST},{input:"\\rho",tag:"mi",output:"\u03C1",ttype:CONST},{input:"\\varrho",tag:"mi",output:"\u03F1",ttype:CONST},{input:"\\varsigma",tag:"mi",output:"\u03C2",ttype:CONST},{input:"\\sigma",tag:"mi",output:"\u03C3",ttype:CONST},{input:"\\tau",tag:"mi",output:"\u03C4",ttype:CONST},{input:"\\upsilon",tag:"mi",output:"\u03C5",ttype:CONST},{input:"\\phi",tag:"mi",output:"\u03C6",ttype:CONST},{input:"\\varphi",tag:"mi",output:"\u03D5",ttype:CONST},{input:"\\chi",tag:"mi",output:"\u03C7",ttype:CONST},{input:"\\psi",tag:"mi",output:"\u03C8",ttype:CONST},{input:"\\omega",tag:"mi",output:"\u03C9",ttype:CONST},{input:"\\Gamma",tag:"mo",output:"\u0393",ttype:CONST},{input:"\\Delta",tag:"mo",output:"\u0394",ttype:CONST},{input:"\\Theta",tag:"mo",output:"\u0398",ttype:CONST},{input:"\\Lambda",tag:"mo",output:"\u039B",ttype:CONST},{input:"\\Xi",tag:"mo",output:"\u039E",ttype:CONST},{input:"\\Pi",tag:"mo",output:"\u03A0",ttype:CONST},{input:"\\Sigma",tag:"mo",output:"\u03A3",ttype:CONST},{input:"\\Upsilon",tag:"mo",output:"\u03A5",ttype:CONST},{input:"\\Phi",tag:"mo",output:"\u03A6",ttype:CONST},{input:"\\Psi",tag:"mo",output:"\u03A8",ttype:CONST},{input:"\\Omega",tag:"mo",output:"\u03A9",ttype:CONST},{input:"\\frac12",tag:"mo",output:"\u00BD",ttype:CONST},{input:"\\frac14",tag:"mo",output:"\u00BC",ttype:CONST},{input:"\\frac34",tag:"mo",output:"\u00BE",ttype:CONST},{input:"\\frac13",tag:"mo",output:"\u2153",ttype:CONST},{input:"\\frac23",tag:"mo",output:"\u2154",ttype:CONST},{input:"\\frac15",tag:"mo",output:"\u2155",ttype:CONST},{input:"\\frac25",tag:"mo",output:"\u2156",ttype:CONST},{input:"\\frac35",tag:"mo",output:"\u2157",ttype:CONST},{input:"\\frac45",tag:"mo",output:"\u2158",ttype:CONST},{input:"\\frac16",tag:"mo",output:"\u2159",ttype:CONST},{input:"\\frac56",tag:"mo",output:"\u215A",ttype:CONST},{input:"\\frac18",tag:"mo",output:"\u215B",ttype:CONST},{input:"\\frac38",tag:"mo",output:"\u215C",ttype:CONST},{input:"\\frac58",tag:"mo",output:"\u215D",ttype:CONST},{input:"\\frac78",tag:"mo",output:"\u215E",ttype:CONST},{input:"\\pm",tag:"mo",output:"\u00B1",ttype:CONST},{input:"\\mp",tag:"mo",output:"\u2213",ttype:CONST},{input:"\\triangleleft",tag:"mo",output:"\u22B2",ttype:CONST},{input:"\\triangleright",tag:"mo",output:"\u22B3",ttype:CONST},{input:"\\cdot",tag:"mo",output:"\u22C5",ttype:CONST},{input:"\\star",tag:"mo",output:"\u22C6",ttype:CONST},{input:"\\ast",tag:"mo",output:"\u002A",ttype:CONST},{input:"\\times",tag:"mo",output:"\u00D7",ttype:CONST},{input:"\\div",tag:"mo",output:"\u00F7",ttype:CONST},{input:"\\circ",tag:"mo",output:"\u2218",ttype:CONST},{input:"\\bullet",tag:"mo",output:"\u2022",ttype:CONST},{input:"\\oplus",tag:"mo",output:"\u2295",ttype:CONST},{input:"\\ominus",tag:"mo",output:"\u2296",ttype:CONST},{input:"\\otimes",tag:"mo",output:"\u2297",ttype:CONST},{input:"\\bigcirc",tag:"mo",output:"\u25CB",ttype:CONST},{input:"\\oslash",tag:"mo",output:"\u2298",ttype:CONST},{input:"\\odot",tag:"mo",output:"\u2299",ttype:CONST},{input:"\\land",tag:"mo",output:"\u2227",ttype:CONST},{input:"\\wedge",tag:"mo",output:"\u2227",ttype:CONST},{input:"\\lor",tag:"mo",output:"\u2228",ttype:CONST},{input:"\\vee",tag:"mo",output:"\u2228",ttype:CONST},{input:"\\cap",tag:"mo",output:"\u2229",ttype:CONST},{input:"\\cup",tag:"mo",output:"\u222A",ttype:CONST},{input:"\\sqcap",tag:"mo",output:"\u2293",ttype:CONST},{input:"\\sqcup",tag:"mo",output:"\u2294",ttype:CONST},{input:"\\uplus",tag:"mo",output:"\u228E",ttype:CONST},{input:"\\amalg",tag:"mo",output:"\u2210",ttype:CONST},{input:"\\bigtriangleup",tag:"mo",output:"\u25B3",ttype:CONST},{input:"\\bigtriangledown",tag:"mo",output:"\u25BD",ttype:CONST},{input:"\\dag",tag:"mo",output:"\u2020",ttype:CONST},{input:"\\dagger",tag:"mo",output:"\u2020",ttype:CONST},{input:"\\ddag",tag:"mo",output:"\u2021",ttype:CONST},{input:"\\ddagger",tag:"mo",output:"\u2021",ttype:CONST},{input:"\\lhd",tag:"mo",output:"\u22B2",ttype:CONST},{input:"\\rhd",tag:"mo",output:"\u22B3",ttype:CONST},{input:"\\unlhd",tag:"mo",output:"\u22B4",ttype:CONST},{input:"\\unrhd",tag:"mo",output:"\u22B5",ttype:CONST},{input:"\\sum",tag:"mo",output:"\u2211",ttype:UNDEROVER},{input:"\\prod",tag:"mo",output:"\u220F",ttype:UNDEROVER},{input:"\\bigcap",tag:"mo",output:"\u22C2",ttype:UNDEROVER},{input:"\\bigcup",tag:"mo",output:"\u22C3",ttype:UNDEROVER},{input:"\\bigwedge",tag:"mo",output:"\u22C0",ttype:UNDEROVER},{input:"\\bigvee",tag:"mo",output:"\u22C1",ttype:UNDEROVER},{input:"\\bigsqcap",tag:"mo",output:"\u2A05",ttype:UNDEROVER},{input:"\\bigsqcup",tag:"mo",output:"\u2A06",ttype:UNDEROVER},{input:"\\coprod",tag:"mo",output:"\u2210",ttype:UNDEROVER},{input:"\\bigoplus",tag:"mo",output:"\u2A01",ttype:UNDEROVER},{input:"\\bigotimes",tag:"mo",output:"\u2A02",ttype:UNDEROVER},{input:"\\bigodot",tag:"mo",output:"\u2A00",ttype:UNDEROVER},{input:"\\biguplus",tag:"mo",output:"\u2A04",ttype:UNDEROVER},{input:"\\int",tag:"mo",output:"\u222B",ttype:CONST},{input:"\\oint",tag:"mo",output:"\u222E",ttype:CONST},{input:":=",tag:"mo",output:":=",ttype:CONST},{input:"\\lt",tag:"mo",output:"<",ttype:CONST},{input:"\\gt",tag:"mo",output:">",ttype:CONST},{input:"\\ne",tag:"mo",output:"\u2260",ttype:CONST},{input:"\\neq",tag:"mo",output:"\u2260",ttype:CONST},{input:"\\le",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\leq",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\leqslant",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\ge",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\geq",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\geqslant",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\equiv",tag:"mo",output:"\u2261",ttype:CONST},{input:"\\ll",tag:"mo",output:"\u226A",ttype:CONST},{input:"\\gg",tag:"mo",output:"\u226B",ttype:CONST},{input:"\\doteq",tag:"mo",output:"\u2250",ttype:CONST},{input:"\\prec",tag:"mo",output:"\u227A",ttype:CONST},{input:"\\succ",tag:"mo",output:"\u227B",ttype:CONST},{input:"\\preceq",tag:"mo",output:"\u227C",ttype:CONST},{input:"\\succeq",tag:"mo",output:"\u227D",ttype:CONST},{input:"\\subset",tag:"mo",output:"\u2282",ttype:CONST},{input:"\\supset",tag:"mo",output:"\u2283",ttype:CONST},{input:"\\subseteq",tag:"mo",output:"\u2286",ttype:CONST},{input:"\\supseteq",tag:"mo",output:"\u2287",ttype:CONST},{input:"\\sqsubset",tag:"mo",output:"\u228F",ttype:CONST},{input:"\\sqsupset",tag:"mo",output:"\u2290",ttype:CONST},{input:"\\sqsubseteq",tag:"mo",output:"\u2291",ttype:CONST},{input:"\\sqsupseteq",tag:"mo",output:"\u2292",ttype:CONST},{input:"\\sim",tag:"mo",output:"\u223C",ttype:CONST},{input:"\\simeq",tag:"mo",output:"\u2243",ttype:CONST},{input:"\\approx",tag:"mo",output:"\u2248",ttype:CONST},{input:"\\cong",tag:"mo",output:"\u2245",ttype:CONST},{input:"\\Join",tag:"mo",output:"\u22C8",ttype:CONST},{input:"\\bowtie",tag:"mo",output:"\u22C8",ttype:CONST},{input:"\\in",tag:"mo",output:"\u2208",ttype:CONST},{input:"\\ni",tag:"mo",output:"\u220B",ttype:CONST},{input:"\\owns",tag:"mo",output:"\u220B",ttype:CONST},{input:"\\propto",tag:"mo",output:"\u221D",ttype:CONST},{input:"\\vdash",tag:"mo",output:"\u22A2",ttype:CONST},{input:"\\dashv",tag:"mo",output:"\u22A3",ttype:CONST},{input:"\\models",tag:"mo",output:"\u22A8",ttype:CONST},{input:"\\perp",tag:"mo",output:"\u22A5",ttype:CONST},{input:"\\smile",tag:"mo",output:"\u2323",ttype:CONST},{input:"\\frown",tag:"mo",output:"\u2322",ttype:CONST},{input:"\\asymp",tag:"mo",output:"\u224D",ttype:CONST},{input:"\\notin",tag:"mo",output:"\u2209",ttype:CONST},{input:"\\begin{eqnarray}",output:"X",ttype:MATRIX,invisible:true},{input:"\\begin{array}",output:"X",ttype:MATRIX,invisible:true},{input:"\\\\",output:"}&{",ttype:DEFINITION},{input:"\\end{eqnarray}",output:"}}",ttype:DEFINITION},{input:"\\end{array}",output:"}}",ttype:DEFINITION},{input:"\\big",tag:"mo",output:"X",atval:"1.2",ieval:"2.2",ttype:BIG},{input:"\\Big",tag:"mo",output:"X",atval:"1.6",ieval:"2.6",ttype:BIG},{input:"\\bigg",tag:"mo",output:"X",atval:"2.2",ieval:"3.2",ttype:BIG},{input:"\\Bigg",tag:"mo",output:"X",atval:"2.9",ieval:"3.9",ttype:BIG},{input:"\\left",tag:"mo",output:"X",ttype:LEFTBRACKET},{input:"\\right",tag:"mo",output:"X",ttype:RIGHTBRACKET},{input:"{",output:"{",ttype:LEFTBRACKET,invisible:true},{input:"}",output:"}",ttype:RIGHTBRACKET,invisible:true},{input:"(",tag:"mo",output:"(",atval:"1",ttype:STRETCHY},{input:"[",tag:"mo",output:"[",atval:"1",ttype:STRETCHY},{input:"\\lbrack",tag:"mo",output:"[",atval:"1",ttype:STRETCHY},{input:"\\{",tag:"mo",output:"{",atval:"1",ttype:STRETCHY},{input:"\\lbrace",tag:"mo",output:"{",atval:"1",ttype:STRETCHY},{input:"\\langle",tag:"mo",output:"\u2329",atval:"1",ttype:STRETCHY},{input:"\\lfloor",tag:"mo",output:"\u230A",atval:"1",ttype:STRETCHY},{input:"\\lceil",tag:"mo",output:"\u2308",atval:"1",ttype:STRETCHY},{input:")",tag:"mo",output:")",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"]",tag:"mo",output:"]",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rbrack",tag:"mo",output:"]",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\}",tag:"mo",output:"}",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rbrace",tag:"mo",output:"}",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rangle",tag:"mo",output:"\u232A",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rfloor",tag:"mo",output:"\u230B",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rceil",tag:"mo",output:"\u2309",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"|",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\|",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"\\vert",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\Vert",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"\\mid",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\parallel",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"/",tag:"mo",output:"/",atval:"1.01",ttype:STRETCHY},{input:"\\backslash",tag:"mo",output:"\u2216",atval:"1",ttype:STRETCHY},{input:"\\setminus",tag:"mo",output:"\\",ttype:CONST},{input:"\\!",tag:"mspace",atname:"width",atval:"-0.167em",ttype:SPACE},{input:"\\,",tag:"mspace",atname:"width",atval:"0.167em",ttype:SPACE},{input:"\\>",tag:"mspace",atname:"width",atval:"0.222em",ttype:SPACE},{input:"\\:",tag:"mspace",atname:"width",atval:"0.222em",ttype:SPACE},{input:"\\;",tag:"mspace",atname:"width",atval:"0.278em",ttype:SPACE},{input:"~",tag:"mspace",atname:"width",atval:"0.333em",ttype:SPACE},{input:"\\quad",tag:"mspace",atname:"width",atval:"1em",ttype:SPACE},{input:"\\qquad",tag:"mspace",atname:"width",atval:"2em",ttype:SPACE},{input:"\\prime",tag:"mo",output:"\u2032",ttype:CONST},{input:"'",tag:"mo",output:"\u02B9",ttype:CONST},{input:"''",tag:"mo",output:"\u02BA",ttype:CONST},{input:"'''",tag:"mo",output:"\u2034",ttype:CONST},{input:"''''",tag:"mo",output:"\u2057",ttype:CONST},{input:"\\ldots",tag:"mo",output:"\u2026",ttype:CONST},{input:"\\cdots",tag:"mo",output:"\u22EF",ttype:CONST},{input:"\\vdots",tag:"mo",output:"\u22EE",ttype:CONST},{input:"\\ddots",tag:"mo",output:"\u22F1",ttype:CONST},{input:"\\forall",tag:"mo",output:"\u2200",ttype:CONST},{input:"\\exists",tag:"mo",output:"\u2203",ttype:CONST},{input:"\\Re",tag:"mo",output:"\u211C",ttype:CONST},{input:"\\Im",tag:"mo",output:"\u2111",ttype:CONST},{input:"\\aleph",tag:"mo",output:"\u2135",ttype:CONST},{input:"\\hbar",tag:"mo",output:"\u210F",ttype:CONST},{input:"\\ell",tag:"mo",output:"\u2113",ttype:CONST},{input:"\\wp",tag:"mo",output:"\u2118",ttype:CONST},{input:"\\emptyset",tag:"mo",output:"\u2205",ttype:CONST},{input:"\\infty",tag:"mo",output:"\u221E",ttype:CONST},{input:"\\surd",tag:"mo",output:"\\sqrt{}",ttype:DEFINITION},{input:"\\partial",tag:"mo",output:"\u2202",ttype:CONST},{input:"\\nabla",tag:"mo",output:"\u2207",ttype:CONST},{input:"\\triangle",tag:"mo",output:"\u25B3",ttype:CONST},{input:"\\therefore",tag:"mo",output:"\u2234",ttype:CONST},{input:"\\angle",tag:"mo",output:"\u2220",ttype:CONST},{input:"\\diamond",tag:"mo",output:"\u22C4",ttype:CONST},{input:"\\Diamond",tag:"mo",output:"\u25C7",ttype:CONST},{input:"\\neg",tag:"mo",output:"\u00AC",ttype:CONST},{input:"\\lnot",tag:"mo",output:"\u00AC",ttype:CONST},{input:"\\bot",tag:"mo",output:"\u22A5",ttype:CONST},{input:"\\top",tag:"mo",output:"\u22A4",ttype:CONST},{input:"\\square",tag:"mo",output:"\u25AB",ttype:CONST},{input:"\\Box",tag:"mo",output:"\u25A1",ttype:CONST},{input:"\\wr",tag:"mo",output:"\u2240",ttype:CONST},{input:"\\arccos",tag:"mi",output:"arccos",ttype:UNARY,func:true},{input:"\\arcsin",tag:"mi",output:"arcsin",ttype:UNARY,func:true},{input:"\\arctan",tag:"mi",output:"arctan",ttype:UNARY,func:true},{input:"\\arg",tag:"mi",output:"arg",ttype:UNARY,func:true},{input:"\\cos",tag:"mi",output:"cos",ttype:UNARY,func:true},{input:"\\cosh",tag:"mi",output:"cosh",ttype:UNARY,func:true},{input:"\\cot",tag:"mi",output:"cot",ttype:UNARY,func:true},{input:"\\coth",tag:"mi",output:"coth",ttype:UNARY,func:true},{input:"\\csc",tag:"mi",output:"csc",ttype:UNARY,func:true},{input:"\\deg",tag:"mi",output:"deg",ttype:UNARY,func:true},{input:"\\det",tag:"mi",output:"det",ttype:UNARY,func:true},{input:"\\dim",tag:"mi",output:"dim",ttype:UNARY,func:true},{input:"\\exp",tag:"mi",output:"exp",ttype:UNARY,func:true},{input:"\\gcd",tag:"mi",output:"gcd",ttype:UNARY,func:true},{input:"\\hom",tag:"mi",output:"hom",ttype:UNARY,func:true},{input:"\\inf",tag:"mo",output:"inf",ttype:UNDEROVER},{input:"\\ker",tag:"mi",output:"ker",ttype:UNARY,func:true},{input:"\\lg",tag:"mi",output:"lg",ttype:UNARY,func:true},{input:"\\lim",tag:"mo",output:"lim",ttype:UNDEROVER},{input:"\\liminf",tag:"mo",output:"liminf",ttype:UNDEROVER},{input:"\\limsup",tag:"mo",output:"limsup",ttype:UNDEROVER},{input:"\\ln",tag:"mi",output:"ln",ttype:UNARY,func:true},{input:"\\log",tag:"mi",output:"log",ttype:UNARY,func:true},{input:"\\max",tag:"mo",output:"max",ttype:UNDEROVER},{input:"\\min",tag:"mo",output:"min",ttype:UNDEROVER},{input:"\\Pr",tag:"mi",output:"Pr",ttype:UNARY,func:true},{input:"\\sec",tag:"mi",output:"sec",ttype:UNARY,func:true},{input:"\\sin",tag:"mi",output:"sin",ttype:UNARY,func:true},{input:"\\sinh",tag:"mi",output:"sinh",ttype:UNARY,func:true},{input:"\\sup",tag:"mo",output:"sup",ttype:UNDEROVER},{input:"\\tan",tag:"mi",output:"tan",ttype:UNARY,func:true},{input:"\\tanh",tag:"mi",output:"tanh",ttype:UNARY,func:true},{input:"\\gets",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\leftarrow",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\to",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\rightarrow",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\leftrightarrow",tag:"mo",output:"\u2194",ttype:CONST},{input:"\\uparrow",tag:"mo",output:"\u2191",ttype:CONST},{input:"\\downarrow",tag:"mo",output:"\u2193",ttype:CONST},{input:"\\updownarrow",tag:"mo",output:"\u2195",ttype:CONST},{input:"\\Leftarrow",tag:"mo",output:"\u21D0",ttype:CONST},{input:"\\Rightarrow",tag:"mo",output:"\u21D2",ttype:CONST},{input:"\\Leftrightarrow",tag:"mo",output:"\u21D4",ttype:CONST},{input:"\\iff",tag:"mo",output:"~\\Longleftrightarrow~",ttype:DEFINITION},{input:"\\Uparrow",tag:"mo",output:"\u21D1",ttype:CONST},{input:"\\Downarrow",tag:"mo",output:"\u21D3",ttype:CONST},{input:"\\Updownarrow",tag:"mo",output:"\u21D5",ttype:CONST},{input:"\\mapsto",tag:"mo",output:"\u21A6",ttype:CONST},{input:"\\longleftarrow",tag:"mo",output:"\u2190",ttype:LONG},{input:"\\longrightarrow",tag:"mo",output:"\u2192",ttype:LONG},{input:"\\longleftrightarrow",tag:"mo",output:"\u2194",ttype:LONG},{input:"\\Longleftarrow",tag:"mo",output:"\u21D0",ttype:LONG},{input:"\\Longrightarrow",tag:"mo",output:"\u21D2",ttype:LONG},{input:"\\Longleftrightarrow",tag:"mo",output:"\u21D4",ttype:LONG},{input:"\\longmapsto",tag:"mo",output:"\u21A6",ttype:CONST},LMsqrt,LMroot,LMfrac,LMover,LMsub,LMsup,LMtext,LMmbox,LMatop,LMchoose,{input:"\\acute",tag:"mover",output:"\u00B4",ttype:UNARY,acc:true},{input:"\\grave",tag:"mover",output:"\u0060",ttype:UNARY,acc:true},{input:"\\breve",tag:"mover",output:"\u02D8",ttype:UNARY,acc:true},{input:"\\check",tag:"mover",output:"\u02C7",ttype:UNARY,acc:true},{input:"\\dot",tag:"mover",output:".",ttype:UNARY,acc:true},{input:"\\ddot",tag:"mover",output:"..",ttype:UNARY,acc:true},{input:"\\mathring",tag:"mover",output:"\u00B0",ttype:UNARY,acc:true},{input:"\\vec",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overrightarrow",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overleftarrow",tag:"mover",output:"\u20D6",ttype:UNARY,acc:true},{input:"\\hat",tag:"mover",output:"\u005E",ttype:UNARY,acc:true},{input:"\\widehat",tag:"mover",output:"\u0302",ttype:UNARY,acc:true},{input:"\\tilde",tag:"mover",output:"~",ttype:UNARY,acc:true},{input:"\\widetilde",tag:"mover",output:"\u02DC",ttype:UNARY,acc:true},{input:"\\bar",tag:"mover",output:"\u203E",ttype:UNARY,acc:true},{input:"\\overbrace",tag:"mover",output:"\u23B4",ttype:UNARY,acc:true},{input:"\\overline",tag:"mover",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\underbrace",tag:"munder",output:"\u23B5",ttype:UNARY,acc:true},{input:"\\underline",tag:"munder",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\displaystyle",tag:"mstyle",atname:"displaystyle",atval:"true",ttype:UNARY},{input:"\\textstyle",tag:"mstyle",atname:"displaystyle",atval:"false",ttype:UNARY},{input:"\\scriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"1",ttype:UNARY},{input:"\\scriptscriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"2",ttype:UNARY},{input:"\\textrm",tag:"mstyle",output:"\\mathrm",ttype:DEFINITION},{input:"\\mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\textbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\mathit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\textit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\texttt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",ttype:UNARY},{input:"\\mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",ttype:UNARY,codes:LMbbb},{input:"\\mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",ttype:UNARY,codes:LMcal},{input:"\\mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",ttype:UNARY,codes:LMfrk}];function compareNames(g,f){if(g.input>f.input){return 1;}else{return -1;}}var LMnames=[];function LMinitSymbols(){LMsymbols.sort(compareNames);for(i=0;i>1;if(g[f]=LMnames[f];}LMpreviousSymbol=LMcurrentSymbol;if(m!=""){LMcurrentSymbol=LMsymbols[l].ttype;return LMsymbols[l];}LMcurrentSymbol=CONST;f=1;s=q.slice(0,1);if("0"<=s&&s<="9"){r="mn";}else{r=(("A">s||s>"Z")&&("a">s||s>"z")?"mo":"mi");}return{input:s,tag:r,output:s,ttype:CONST};}var LMpreviousSymbol,LMcurrentSymbol;function LMparseSexpr(v){var z,w,q,f,D,s,r=document.createDocumentFragment();v=LMremoveCharsAndBlanks(v,0);z=LMgetSymbol(v);if(z==null||z.ttype==RIGHTBRACKET){return[null,v,null];}if(z.ttype==DEFINITION){v=z.output+LMremoveCharsAndBlanks(v,z.input.length);z=LMgetSymbol(v);if(z==null||z.ttype==RIGHTBRACKET){return[null,v,null];}}v=LMremoveCharsAndBlanks(v,z.input.length);switch(z.ttype){case SPACE:w=LMcreateElementMathML(z.tag);w.setAttribute(z.atname,z.atval);return[w,v,z.tag];case UNDEROVER:if(isIE){if(z.input.substr(0,4)=="\\big"){v="\\"+z.input.substr(4)+v;z=LMgetSymbol(v);z.ttype=UNDEROVER;v=LMremoveCharsAndBlanks(v,z.input.length);}}return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];case CONST:var m=z.output;if(isIE){if(z.input=="'"){m="\u2032";}else{if(z.input=="''"){m="\u2033";}else{if(z.input=="'''"){m="\u2033\u2032";}else{if(z.input=="''''"){m="\u2033\u2033";}else{if(z.input=="\\square"){m="\u25A1";}else{if(z.input.substr(0,5)=="\\frac"){var h=z.input.substr(6,1);if(h=="5"||h=="6"){v=z.input.replace(/\\frac/,"\\frac ")+v;return[w,v,z.tag];}}}}}}}}w=LMcreateMmlNode(z.tag,document.createTextNode(m));return[w,v,z.tag];case LONG:w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));w.setAttribute("minsize","1.5");w.setAttribute("maxsize","1.5");w=LMcreateMmlNode("mover",w);w.appendChild(LMcreateElementMathML("mspace"));return[w,v,z.tag];case STRETCHY:if(isIE&&z.input=="\\backslash"){z.output="\\";}w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));if(z.input=="|"||z.input=="\\vert"||z.input=="\\|"||z.input=="\\Vert"){w.setAttribute("lspace","0em");w.setAttribute("rspace","0em");}w.setAttribute("maxsize",z.atval);if(z.rtag!=null){return[w,v,z.rtag];}else{return[w,v,z.tag];}case BIG:var l=z.atval;if(isIE){l=z.ieval;}z=LMgetSymbol(v);if(z==null){return[null,v,null];}v=LMremoveCharsAndBlanks(v,z.input.length);w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("height",l+"ex");w=LMcreateMmlNode("mrow",w);w.appendChild(F);}else{w.setAttribute("minsize",l);w.setAttribute("maxsize",l);}return[w,v,z.tag];case LEFTBRACKET:if(z.input=="\\left"){z=LMgetSymbol(v);if(z!=null){if(z.input=="."){z.invisible=true;}v=LMremoveCharsAndBlanks(v,z.input.length);}}q=LMparseExpr(v,true,false);if(z==null||(typeof z.invisible=="boolean"&&z.invisible)){w=LMcreateMmlNode("mrow",q[0]);}else{w=LMcreateMmlNode("mo",document.createTextNode(z.output));w=LMcreateMmlNode("mrow",w);w.appendChild(q[0]);}return[w,q[1],q[2]];case MATRIX:if(z.input=="\\begin{array}"){var B="";z=LMgetSymbol(v);v=LMremoveCharsAndBlanks(v,0);if(z==null){B="l";}else{v=LMremoveCharsAndBlanks(v,z.input.length);if(z.input!="{"){B="l";}else{do{z=LMgetSymbol(v);if(z!=null){v=LMremoveCharsAndBlanks(v,z.input.length);if(z.input!="}"){B=B+z.input;}}}while(z!=null&&z.input!=""&&z.input!="}");}}q=LMparseExpr("{"+v,true,true);w=LMcreateMmlNode("mtable",q[0]);B=B.replace(/l/g,"left ");B=B.replace(/r/g,"right ");B=B.replace(/c/g,"center ");w.setAttribute("columnalign",B);w.setAttribute("displaystyle","false");if(isIE){return[w,q[1],null];}var k=LMcreateElementMathML("mspace");k.setAttribute("width","0.167em");var E=LMcreateElementMathML("mspace");E.setAttribute("width","0.167em");var g=LMcreateMmlNode("mrow",k);g.appendChild(w);g.appendChild(E);return[g,q[1],null];}else{q=LMparseExpr("{"+v,true,true);w=LMcreateMmlNode("mtable",q[0]);if(isIE){w.setAttribute("columnspacing","0.25em");}else{w.setAttribute("columnspacing","0.167em");}w.setAttribute("columnalign","right center left");w.setAttribute("displaystyle","true");w=LMcreateMmlNode("mrow",w);return[w,q[1],null];}case TEXT:if(v.charAt(0)=="{"){D=v.indexOf("}");}else{D=0;}if(D==-1){D=v.length;}s=v.slice(1,D);if(s.charAt(0)==" "){w=LMcreateElementMathML("mspace");w.setAttribute("width","0.33em");r.appendChild(w);}r.appendChild(LMcreateMmlNode(z.tag,document.createTextNode(s)));if(s.charAt(s.length-1)==" "){w=LMcreateElementMathML("mspace");w.setAttribute("width","0.33em");r.appendChild(w);}v=LMremoveCharsAndBlanks(v,D+1);return[LMcreateMmlNode("mrow",r),v,null];case UNARY:q=LMparseSexpr(v);if(q[0]==null){return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v];}if(typeof z.func=="boolean"&&z.func){s=v.charAt(0);if(s=="^"||s=="_"||s==","){return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];}else{w=LMcreateMmlNode("mrow",LMcreateMmlNode(z.tag,document.createTextNode(z.output)));if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("width","0.167em");w.appendChild(F);}w.appendChild(q[0]);return[w,q[1],z.tag];}}if(z.input=="\\sqrt"){if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("height","1.2ex");F.setAttribute("width","0em");w=LMcreateMmlNode(z.tag,q[0]);w.appendChild(F);return[w,q[1],z.tag];}else{return[LMcreateMmlNode(z.tag,q[0]),q[1],z.tag];}}else{if(typeof z.acc=="boolean"&&z.acc){w=LMcreateMmlNode(z.tag,q[0]);var m=z.output;if(isIE){if(z.input=="\\hat"){m="\u0302";}else{if(z.input=="\\widehat"){m="\u005E";}else{if(z.input=="\\bar"){m="\u00AF";}else{if(z.input=="\\grave"){m="\u0300";}else{if(z.input=="\\tilde"){m="\u0303";}}}}}}var g=LMcreateMmlNode("mo",document.createTextNode(m));if(z.input=="\\vec"||z.input=="\\check"){g.setAttribute("maxsize","1.2");}if(isIE&&z.input=="\\bar"){g.setAttribute("maxsize","0.5");}if(z.input=="\\underbrace"||z.input=="\\underline"){g.setAttribute("accentunder","true");}else{g.setAttribute("accent","true");}w.appendChild(g);if(z.input=="\\overbrace"||z.input=="\\underbrace"){w.ttype=UNDEROVER;}return[w,q[1],z.tag];}else{if(!isIE&&typeof z.codes!="undefined"){for(D=0;D64&&s.charCodeAt(A)<91){o=o+String.fromCharCode(z.codes[s.charCodeAt(A)-65]);}else{o=o+s.charAt(A);}}if(q[0].nodeName=="mi"){q[0]=LMcreateElementMathML("mo").appendChild(document.createTextNode(o));}else{q[0].replaceChild(LMcreateElementMathML("mo").appendChild(document.createTextNode(o)),q[0].childNodes[D]);}}}}w=LMcreateMmlNode(z.tag,q[0]);w.setAttribute(z.atname,z.atval);if(z.input=="\\scriptstyle"||z.input=="\\scriptscriptstyle"){w.setAttribute("displaystyle","false");}return[w,q[1],z.tag];}}case BINARY:q=LMparseSexpr(v);if(q[0]==null){return[LMcreateMmlNode("mo",document.createTextNode(z.input)),v,null];}f=LMparseSexpr(q[1]);if(f[0]==null){return[LMcreateMmlNode("mo",document.createTextNode(z.input)),v,null];}if(z.input=="\\root"||z.input=="\\stackrel"){r.appendChild(f[0]);}r.appendChild(q[0]);if(z.input=="\\frac"){r.appendChild(f[0]);}return[LMcreateMmlNode(z.tag,r),f[1],z.tag];case INFIX:v=LMremoveCharsAndBlanks(v,z.input.length);return[LMcreateMmlNode("mo",document.createTextNode(z.output)),v,z.tag];default:return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];}}function LMparseIexpr(l){var k,h,g,j,o,q,m;l=LMremoveCharsAndBlanks(l,0);h=LMgetSymbol(l);o=LMparseSexpr(l);j=o[0];l=o[1];q=o[2];k=LMgetSymbol(l);if(k.ttype==INFIX){l=LMremoveCharsAndBlanks(l,k.input.length);o=LMparseSexpr(l);if(o[0]==null){o[0]=LMcreateMmlNode("mo",document.createTextNode("\u25A1"));}l=o[1];q=o[2];if(k.input=="_"||k.input=="^"){g=LMgetSymbol(l);q=null;m=((h.ttype==UNDEROVER)||(j.ttype==UNDEROVER));if(k.input=="_"&&g.input=="^"){l=LMremoveCharsAndBlanks(l,g.input.length);var f=LMparseSexpr(l);l=f[1];q=f[2];j=LMcreateMmlNode((m?"munderover":"msubsup"),j);j.appendChild(o[0]);j.appendChild(f[0]);}else{if(k.input=="_"){j=LMcreateMmlNode((m?"munder":"msub"),j);j.appendChild(o[0]);}else{j=LMcreateMmlNode((m?"mover":"msup"),j);j.appendChild(o[0]);}}j=LMcreateMmlNode("mrow",j);}else{j=LMcreateMmlNode(k.tag,j);if(k.input=="\\atop"||k.input=="\\choose"){j.setAttribute("linethickness","0ex");}j.appendChild(o[0]);if(k.input=="\\choose"){j=LMcreateMmlNode("mfenced",j);}}}return[j,l,q];}function LMparseExpr(s,r,B){var A,v,l,E,I,o=document.createDocumentFragment();do{s=LMremoveCharsAndBlanks(s,0);l=LMparseIexpr(s);v=l[0];s=l[1];I=l[2];A=LMgetSymbol(s);if(v!=undefined){if((I=="mn"||I=="mi")&&A!=null&&typeof A.func=="boolean"&&A.func){var H=LMcreateElementMathML("mspace");H.setAttribute("width","0.167em");v=LMcreateMmlNode("mrow",v);v.appendChild(H);}o.appendChild(v);}}while((A.ttype!=RIGHTBRACKET)&&A!=null&&A.output!="");I=null;if(A.ttype==RIGHTBRACKET){if(A.input=="\\right"){s=LMremoveCharsAndBlanks(s,A.input.length);A=LMgetSymbol(s);if(A!=null&&A.input=="."){A.invisible=true;}if(A!=null){I=A.rtag;}}if(A!=null){s=LMremoveCharsAndBlanks(s,A.input.length);}var F=o.childNodes.length;if(B&&F>0&&o.childNodes[F-1].nodeName=="mrow"&&F>1&&o.childNodes[F-2].nodeName=="mo"&&o.childNodes[F-2].firstChild.nodeValue=="&"){var g=[];var w=o.childNodes.length;for(E=0;B&&E2){o.removeChild(o.firstChild);o.removeChild(o.firstChild);}G.appendChild(LMcreateMmlNode("mtr",h));}return[G,s];}if(typeof A.invisible!="boolean"||!A.invisible){v=LMcreateMmlNode("mo",document.createTextNode(A.output));o.appendChild(v);}}return[o,s,I];}function LMparseMath(j){var f,h=LMcreateElementMathML("mstyle");if(LMmathcolor!=""){h.setAttribute("mathcolor",LMmathcolor);}if(LMmathfontfamily!=""){h.setAttribute("fontfamily",LMmathfontfamily);}h.appendChild(LMparseExpr(j.replace(/^\s+/g,""),false,false)[0]);h=LMcreateMmlNode("math",h);if(LMshowasciiformulaonhover){h.setAttribute("title",j.replace(/\s+/g," "));}var g=LMcreateElementXHTML("span");g.style.fontSize=mathfontsize;if(LMmathfontfamily!=""){g.style.fontFamily=LMmathfontfamily;}g.appendChild(h);return g;}function LMstrarr2docFrag(f,k){var o=document.createDocumentFragment();var m=false;for(var l=0;l1||q){if(LMcheckForMathML){LMcheckForMathML=false;var h=LMisMathMLavailable();LMnoMathML=h!=null;if(LMnoMathML&&LMnotifyIfNoMathML){if(LMalertIfNoMathML){alert("To view the ASCIIMathML notation use Internet Explorer 6 +\nMathPlayer (free from www.dessci.com)\n or Firefox/Mozilla/Netscape");}else{LMbody.insertBefore(h,LMbody.childNodes[0]);}}}if(!LMnoMathML){f=LMstrarr2docFrag(k,g.nodeType==8);var l=f.childNodes.length;g.parentNode.replaceChild(f,g);return l-1;}else{return 0;}}}}else{return 0;}}else{if(g.nodeName!="math"){for(j=0;j$\\displaystyle{$1}$

');f=f.replace(/\\begin{(theorem|lemma|proposition|corollary)}((.|\n)*?)\\end{\1}/g,function(j,h,g){tcnt++;return""+h.charAt(0).toUpperCase()+h.slice(1)+" "+tcnt+". "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+"";});f=f.replace(/\\begin{(definition|example|remark|problem|exercise|conjecture|solution)}((.|\n)*?)\\end{\1}/g,function(j,h,g){dcnt++;return""+h.charAt(0).toUpperCase()+h.slice(1)+" "+dcnt+". "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"");});f=f.replace(/\\begin{proof}((.|\n)*?)\\end{proof}/g,function(h,g){return"Proof: "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+" □";});f=f.replace(/\\emph{(.*?)}/g,"$1");f=f.replace(/\\textbf{(.*?)}/g,"$1");f=f.replace(/\\cite{(.*?)}/g,"[$1]");f=f.replace(/\\chapter{(.*?)}/g,"

$1

");f=f.replace(/\\section{(.*?)}(\s*<\/?(br|p)\s?\/?>)?/g,"

$1

");f=f.replace(/\\subsection{(.*?)}/g,"

$1

");f=f.replace(/\\begin{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"
    ");f=f.replace(/\\item\s((.|\n)*?)(?=(\\item|\\end))/g,"
  • $1
    • ");f=f.replace(/\\end{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"
");f=f.replace(/\\begin{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"
    ");f=f.replace(/\\end{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"
");f=f.replace(/\\item\[(.*?)]{(.*?)}/g,"
$1
$2
");f=f.replace(/\\begin{description}/g,"
");f=f.replace(/\\end{description}/g,"
");f=f.replace(/\\newline\b/g,"
");f=f.replace(/\\newpage\b/g,'
');f=f.replace(/\\par\b/g,"

 

");f=f.replace(/\\bigskip/g,'

 

');f=f.replace(/\\medskip/g,'

 

');f=f.replace(/\\smallskip/g,'

 

');f=f.replace(/\\begin{center}(.*?)\\end{center}/g,'

$1

');f=f.replace(//gi,"\n")+"'/>";});f=f.replace(/insertASCIIMathCalculator/g,'
');return f;}function LMprocessNode(o,g,k){var m,f;if(k!=null){m=document.getElementsByTagName("span");for(var h=0;h(.*?)<\/sup>(\s|(\S))/gi,"^{$1} $3");f=f.replace(/(Proof:)/g,"$1");f=f.replace(/QED/g,"□");f=f.replace(/(\\?end{?a?math}?)/ig,"$1");f=f.replace(/(\bamath|\\begin{a?math})/ig,"$1");f=f.replace(/([>\n])(Theorem|Lemma|Proposition|Corollary|Definition|Example|Remark|Problem|Exercise|Conjecture|Solution)(:|\W\W?(\w|\.)*?\W?:)/g,"$1$2$3");}f=f.replace(/%7E/g,"~");if(!avoidinnerHTML){o.innerHTML=f;}LMprocessNodeR(o,g);}}if(isIE){m=document.getElementsByTagName("math");for(var h=0;h');document.write('');}var checkIfSVGavailable=true;var notifyIfNoSVG=true;var alertIfNoSVG=false;var defaultwidth=300;defaultheight=200;var defaultxmin=-5.5;defaultxmax=5.5;var defaultborder=0;border=defaultborder;var defaultstrokewidth="1";var defaultstroke="blue";var defaultstrokeopacity=1;var defaultstrokedasharray=null;var defaultfill="none";var defaultfillopacity=1;var defaultfontstyle="normal";var defaultfontfamily="times";var defaultfontsize="16";var defaultfontweight="normal";var defaultfontstroke="none";var defaultfontfill="none";var defaultmarker="none";var defaultendpoints="";var showcoordinates=true;var markerstrokewidth="1";var markerstroke="black";var markerfill="yellow";var markersize=4;var arrowfill=stroke;var dotradius=4;var ticklength=4;var axesstroke="black";var gridstroke="grey";var backgroundstyle="fill-opacity:0; fill:white";var singlelettersitalic=true;var picturepos=null;var xunitlength;var yunitlength;var origin=[0,0];var above="above";var below="below";var left="left";var right="right";var aboveleft="aboveleft";var aboveright="aboveright";var belowleft="belowleft";var belowright="belowright";var xmin,xmax,ymin,ymax,xscl,yscl,xgrid,ygrid,xtick,ytick,initialized;var strokewidth,strokedasharray,stroke,fill,strokeopacity,fillopacity;var fontstyle,fontfamily,fontsize,fontweight,fontstroke,fontfill;var marker,endpoints,dynamic={};var picture,svgpicture,doc,width,height,a,b,c,d,i,n,p,t,x,y;var isIE=document.createElementNS==null;var cpi="\u03C0",ctheta="\u03B8";var log=function(f){return ln(f)/ln(10);};var pi=Math.PI,e=Math.E,ln=Math.log,sqrt=Math.sqrt;var floor=Math.floor,ceil=Math.ceil,abs=Math.abs;var sin=Math.sin,cos=Math.cos,tan=Math.tan;var arcsin=Math.asin,arccos=Math.acos,arctan=Math.atan;var sec=function(f){return 1/Math.cos(f);};var csc=function(f){return 1/Math.sin(f);};var cot=function(f){return 1/Math.tan(f);};var arcsec=function(f){return arccos(1/f);};var arccsc=function(f){return arcsin(1/f);};var arccot=function(f){return arctan(1/f);};var sinh=function(f){return(Math.exp(f)-Math.exp(-f))/2;};var cosh=function(f){return(Math.exp(f)+Math.exp(-f))/2;};var tanh=function(f){return(Math.exp(f)-Math.exp(-f))/(Math.exp(f)+Math.exp(-f));};var sech=function(f){return 1/cosh(f);};var csch=function(f){return 1/sinh(f);};var coth=function(f){return 1/tanh(f);};var arcsinh=function(f){return ln(f+Math.sqrt(f*f+1));};var arccosh=function(f){return ln(f+Math.sqrt(f*f-1));};var arctanh=function(f){return ln((1+f)/(1-f))/2;};var sech=function(f){return 1/cosh(f);};var csch=function(f){return 1/sinh(f);};var coth=function(f){return 1/tanh(f);};var arcsech=function(f){return arccosh(1/f);};var arccsch=function(f){return arcsinh(1/f);};var arccoth=function(f){return arctanh(1/f);};var sign=function(f){return(f==0?0:(f<0?-1:1));};function factorial(f,h){if(h==null){h=1;}if(Math.abs(f-Math.round(f*1000000)/1000000)<1e-15){f=Math.round(f*1000000)/1000000;}if(f-Math.floor(f)!=0){return NaN;}for(var g=f-h;g>0;g-=h){f*=g;}return(f<0?NaN:(f==0?1:f));}function C(f,g){var j=1;for(var h=0;h0){if(alertIfNoSVG){alert("To view the SVG pictures in Internet Explorer\ndownload the free Adobe SVGviewer from www.adobe.com/svg or\nuse Firefox 2.0 or later");}else{g.insertBefore(m,g.childNodes[0]);}}}if(m==null){for(s=0;s=xmax){alert("Picture requires at least two numbers: xmin < xmax");}else{if(f!=null&&(typeof h!="number"||typeof f!="number"||h>=f)){alert("initPicture(xmin,xmax,ymin,ymax) requires numbers ymin < ymax");}else{if(width==null){width=picture.getAttribute("width");if(width==null||width==""){width=defaultwidth;}}picture.setAttribute("width",width);if(height==null){height=picture.getAttribute("height");if(height==null||height==""){height=defaultheight;}}picture.setAttribute("height",height);xunitlength=(width-2*border)/(xmax-xmin);yunitlength=xunitlength;if(ymin==null){origin=[-xmin*xunitlength+border,height/2];ymin=-(height-2*border)/(2*yunitlength);ymax=-ymin;}else{if(ymax!=null){yunitlength=(height-2*border)/(ymax-ymin);}else{ymax=(height-2*border)/yunitlength+ymin;}origin=[-xmin*xunitlength+border,-ymin*yunitlength+border];}if(isIE){if(picture.FULLSCREEN==undefined){setTimeout("drawPictures()",50);throw"wait";}svgpicture=picture.getSVGDocument().getElementById("root");if(svgpicture==null){setTimeout("drawPictures()",50);throw"wait";}svgpicture=picture.getSVGDocument().getElementById("root");while(svgpicture.childNodes.length>0){svgpicture.removeChild(svgpicture.lastChild);}svgpicture.setAttribute("width",width);svgpicture.setAttribute("height",height);svgpicture.setAttribute("name",picture.getAttribute("id"));doc=picture.getSVGDocument();var l=document.getElementById(picture.getAttribute("id")+"mml");if(l!=null){while(l.childNodes.length>0){l.removeChild(l.lastChild);}}}else{var g=document.createElementNS("http://www.w3.org/2000/svg","svg");g.setAttribute("id",picture.getAttribute("id"));g.setAttribute("name",picture.getAttribute("id"));g.setAttribute("style","display:inline");g.setAttribute("width",picture.getAttribute("width"));g.setAttribute("height",picture.getAttribute("height"));picturepos=findPos(picture);g.setAttribute("left",picturepos[0]);g.setAttribute("top",picturepos[1]);if(picture.parentNode!=null){picture.parentNode.replaceChild(g,picture);}else{svgpicture.parentNode.replaceChild(g,svgpicture);}svgpicture=g;doc=document;}svgpicture.setAttribute("xunitlength",xunitlength);svgpicture.setAttribute("yunitlength",yunitlength);svgpicture.setAttribute("xmin",xmin);svgpicture.setAttribute("xmax",xmax);svgpicture.setAttribute("ymin",ymin);svgpicture.setAttribute("ymax",ymax);svgpicture.setAttribute("ox",origin[0]);svgpicture.setAttribute("oy",origin[1]);var j=myCreateElementSVG("rect");j.setAttribute("x","0");j.setAttribute("y","0");j.setAttribute("width",width);j.setAttribute("height",height);j.setAttribute("style",backgroundstyle);svgpicture.appendChild(j);svgpicture.setAttribute("onmousemove","displayCoord(evt)");svgpicture.setAttribute("onmouseout","removeCoord(evt)");svgpicture.setAttribute("onclick","mClick(evt)");j=myCreateElementSVG("text");j.appendChild(doc.createTextNode(" "));svgpicture.appendChild(j);border=defaultborder;}}}}function line(j,h,k,g){var f;if(k!=null){f=doc.getElementById(k);}if(f==null){f=myCreateElementSVG("path");f.setAttribute("id",k);svgpicture.appendChild(f);}f.setAttribute("d","M"+(j[0]*xunitlength+origin[0])+","+(height-j[1]*yunitlength-origin[1])+" "+(h[0]*xunitlength+origin[0])+","+(height-h[1]*yunitlength-origin[1]));f.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null){f.setAttribute("stroke-dasharray",strokedasharray);}f.setAttribute("stroke",stroke);f.setAttribute("fill",fill);f.setAttribute("stroke-opacity",strokeopacity);f.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot"){ASdot(j,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(j,h);}ASdot(h,markersize,markerstroke,markerfill);}else{if(marker=="arrow"){arrowhead(j,h);}}if(g==null&&endpoints!=""){g=endpoints;}if(g!=null){if(g.indexOf("<-")!=-1){arrowhead(h,j);}if(g.indexOf("o-")!=-1){dot(j,"open");}if(g.indexOf("*-")!=-1){dot(j,"closed");}if(g.indexOf("->")!=-1){arrowhead(j,h);}if(g.indexOf("-o")!=-1){dot(h,"open");}if(g.indexOf("-*")!=-1){dot(h,"closed");}}}function path(k,m,l,j){if(l==null){l="";}var h,f,g;if(m!=null){h=doc.getElementById(m);}if(h==null){h=myCreateElementSVG("path");h.setAttribute("id",m);svgpicture.appendChild(h);}if(typeof k=="string"){f=k;}else{f="M";f+=(k[0][0]*xunitlength+origin[0])+","+(height-k[0][1]*yunitlength-origin[1])+" "+l;for(g=1;g")!=-1){arrowhead(k[k.length-2],k[k.length-1]);}if(j.indexOf("-o")!=-1){dot(k[k.length-1],"open");}if(j.indexOf("-*")!=-1){dot(k[k.length-1],"closed");}}}function curve(g,h,f){path(g,h,"T",f);}function vector(g,f,h){line(g,f,h,"","->");}function circle(g,f,j){var h;if(j!=null){h=doc.getElementById(j);}if(h==null){h=myCreateElementSVG("circle");h.setAttribute("id",j);svgpicture.appendChild(h);}h.setAttribute("cx",g[0]*xunitlength+origin[0]);h.setAttribute("cy",height-g[1]*yunitlength-origin[1]);h.setAttribute("r",f*xunitlength);h.setAttribute("stroke-width",strokewidth);h.setAttribute("stroke",stroke);h.setAttribute("fill",fill);h.setAttribute("stroke-opacity",strokeopacity);h.setAttribute("fill-opacity",fillopacity);}function loop(f,g,h){if(g==null){g=[1,0];}path([f,[f[0]+g[0],f[1]+g[1]],[f[0]-g[1],f[1]+g[0]],f],h,"C");if(marker=="arrow"||marker=="arrowdot"){arrowhead([f[0]+Math.cos(1.4)*g[0]-Math.sin(1.4)*g[1],f[1]+Math.sin(1.4)*g[0]+Math.cos(1.4)*g[1]],f);}}function arc(l,g,f,k){var j,h;if(k!=null){j=doc.getElementById(k);}if(f==null){h=[g[0]-l[0],g[1]-l[1]];f=Math.sqrt(h[0]*h[0]+h[1]*h[1]);}if(j==null){j=myCreateElementSVG("path");j.setAttribute("id",k);svgpicture.appendChild(j);}j.setAttribute("d","M"+(l[0]*xunitlength+origin[0])+","+(height-l[1]*yunitlength-origin[1])+" A"+f*xunitlength+","+f*yunitlength+" 0 0,0 "+(g[0]*xunitlength+origin[0])+","+(height-g[1]*yunitlength-origin[1]));j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);j.setAttribute("fill",fill);j.setAttribute("stroke-opacity",strokeopacity);j.setAttribute("fill-opacity",fillopacity);if(marker=="arrow"||marker=="arrowdot"){u=[(g[1]-l[1])/4,(l[0]-g[0])/4];h=[(g[0]-l[0])/2,(g[1]-l[1])/2];h=[l[0]+h[0]+u[0],l[1]+h[1]+u[1]];}else{h=[l[0],l[1]];}if(marker=="dot"||marker=="arrowdot"){ASdot(l,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(h,g);}ASdot(g,markersize,markerstroke,markerfill);}else{if(marker=="arrow"){arrowhead(h,g);}}}function sector(f,l,g,k){var j=l[0]-f[0],h=l[1]-f[1];arc(l,g,Math.sqrt(j*j+h*h),k+"arc");path([g,f,l],k+"path");}function ellipse(f,j,h,k){var g;if(k!=null){g=doc.getElementById(k);}if(g==null){g=myCreateElementSVG("ellipse");g.setAttribute("id",k);svgpicture.appendChild(g);}g.setAttribute("cx",f[0]*xunitlength+origin[0]);g.setAttribute("cy",height-f[1]*yunitlength-origin[1]);g.setAttribute("rx",j*xunitlength);g.setAttribute("ry",h*yunitlength);g.setAttribute("stroke-width",strokewidth);g.setAttribute("stroke",stroke);g.setAttribute("fill",fill);g.setAttribute("stroke-opacity",strokeopacity);g.setAttribute("fill-opacity",fillopacity);}function triangle(h,g,f,j){path([h,g,f,h],j);}function rect(k,h,l,j,g){var f;if(l!=null){f=doc.getElementById(l);}if(f==null){f=myCreateElementSVG("rect");f.setAttribute("id",l);svgpicture.appendChild(f);}f.setAttribute("x",k[0]*xunitlength+origin[0]);f.setAttribute("y",height-h[1]*yunitlength-origin[1]);f.setAttribute("width",(h[0]-k[0])*xunitlength);f.setAttribute("height",(h[1]-k[1])*yunitlength);if(j!=null){f.setAttribute("rx",j*xunitlength);}if(g!=null){f.setAttribute("ry",g*yunitlength);}f.setAttribute("stroke-width",strokewidth);f.setAttribute("stroke",stroke);f.setAttribute("fill",fill);f.setAttribute("stroke-opacity",strokeopacity);f.setAttribute("fill-opacity",fillopacity);}function text(g,q,l,f,m){var k,j,r=0,o=fontsize/3;if(/(`|\$)/.test(q)){k=document.getElementById(svgpicture.getAttribute("name")+"mml");if(k!=null){if(f!=null){j=document.getElementById(f);}if(j==null){j=myCreateElementXHTML("div");j.setAttribute("id",f);j.style.position="absolute";k.appendChild(j);}while(j.childNodes.length>0){j.removeChild(j.lastChild);}j.appendChild(document.createTextNode(q));j.style.left=""+(g[0]*xunitlength+origin[0])+"px";j.style.top=""+(height-g[1]*yunitlength-origin[1])+"px";if(/`/.test(q)){AMprocessNode(j);}else{LMprocessNode(j);}r=-j.offsetWidth/2;o=-j.offsetHeight/2;if(l!=null){if(/above/.test(l)){o=-j.offsetHeight;}if(/below/.test(l)){o=0;}if(/right/.test(l)){r=0;}if(/left/.test(l)){r=-j.offsetWidth;}}j.style.left=""+(g[0]*xunitlength+origin[0]+r)+"px";j.style.top=""+(height-g[1]*yunitlength-origin[1]+o)+"px";}return g;}var h="middle";if(l!=null){if(/above/.test(l)){o=-fontsize/2;}if(/below/.test(l)){o=fontsize-0;}if(/right/.test(l)){h="start";r=fontsize/4;}if(/left/.test(l)){h="end";r=-fontsize/4;}}if(f!=null){j=doc.getElementById(f);}if(j==null){j=myCreateElementSVG("text");j.setAttribute("id",f);svgpicture.appendChild(j);j.appendChild(doc.createTextNode(q));}while(j.childNodes.length>1){j.removeChild(j.lastChild);}j.lastChild.nodeValue="\xA0"+q+"\xA0";j.setAttribute("x",g[0]*xunitlength+origin[0]+r);j.setAttribute("y",height-g[1]*yunitlength-origin[1]+o);j.setAttribute("font-style",(m!=null?m:(q.search(/^[a-zA-Z]$/)!=-1?"italic":fontstyle)));j.setAttribute("font-family",fontfamily);j.setAttribute("font-size",fontsize);j.setAttribute("font-weight",fontweight);j.setAttribute("text-anchor",h);if(fontstroke!="none"){j.setAttribute("stroke",fontstroke);}if(fontfill!="none"){j.setAttribute("fill",fontfill);}return g;}function mtext(l,h,o,m){var j="middle";var g=0;var f=fontsize/3;if(o!=null){if(o.slice(0,5)=="above"){f=-fontsize/2;}if(o.slice(0,5)=="below"){f=fontsize-0;}if(o.slice(0,5)=="right"||o.slice(5,10)=="right"){j="start";g=fontsize/2;}if(o.slice(0,4)=="left"||o.slice(5,9)=="left"){j="end";g=-fontsize/2;}}var k=this;if(this.nodeName=="svg"){k=myCreateElementSVG("text");this.appendChild(k);k.appendChild(doc.createTextNode(h));}k.lastChild.nodeValue=h;k.setAttribute("x",l[0]+g);k.setAttribute("y",l[1]+f);k.setAttribute("font-style",(m!=null?m:fontstyle));k.setAttribute("font-family",fontfamily);k.setAttribute("font-size",fontsize);k.setAttribute("font-weight",fontweight);k.setAttribute("text-anchor",j);if(fontstroke!="none"){k.setAttribute("stroke",fontstroke);}if(fontfill!="none"){k.setAttribute("fill",fontfill);}}function image(g,l,f,j,m){var k;if(m!=null){k=doc.getElementById(m);}if(k==null){k=myCreateElementSVG("image");k.setAttribute("id",m);svgpicture.appendChild(k);}k.setAttribute("x",l[0]*xunitlength+origin[0]);k.setAttribute("y",height-l[1]*yunitlength-origin[1]);k.setAttribute("width",f);k.setAttribute("height",j);k.setAttribute("xlink:href",g);}function ASdot(h,g,j,l){if(j==null){j=stroke;}if(l==null){l=fill;}var k=myCreateElementSVG("circle");k.setAttribute("cx",h[0]*xunitlength+origin[0]);k.setAttribute("cy",height-h[1]*yunitlength-origin[1]);k.setAttribute("r",g);k.setAttribute("stroke-width",strokewidth);k.setAttribute("stroke",j);k.setAttribute("fill",l);svgpicture.appendChild(k);}function dot(g,k,h,o,m){var j;var f=g[0]*xunitlength+origin[0];var l=height-g[1]*yunitlength-origin[1];if(m!=null){j=doc.getElementById(m);}if(k=="+"||k=="-"||k=="|"){if(j==null){j=myCreateElementSVG("path");j.setAttribute("id",m);svgpicture.appendChild(j);}if(k=="+"){j.setAttribute("d"," M "+(f-ticklength)+" "+l+" L "+(f+ticklength)+" "+l+" M "+f+" "+(l-ticklength)+" L "+f+" "+(l+ticklength));j.setAttribute("stroke-width",0.5);j.setAttribute("stroke",axesstroke);}else{if(k=="-"){j.setAttribute("d"," M "+(f-ticklength)+" "+l+" L "+(f+ticklength)+" "+l);}else{j.setAttribute("d"," M "+f+" "+(l-ticklength)+" L "+f+" "+(l+ticklength));}j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);}}else{if(j==null){j=myCreateElementSVG("circle");j.setAttribute("id",m);svgpicture.appendChild(j);}j.setAttribute("cx",f);j.setAttribute("cy",l);j.setAttribute("r",dotradius);j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);j.setAttribute("fill",(k=="open"?"white":(k=="closed"?stroke:markerfill)));}if(h!=null){text(g,h,(o==null?"below":o),(m==null?m:m+"label"));}}point=dot;function arrowhead(m,l){var f;var h=[m[0]*xunitlength+origin[0],height-m[1]*yunitlength-origin[1]];var g=[l[0]*xunitlength+origin[0],height-l[1]*yunitlength-origin[1]];var j=[g[0]-h[0],g[1]-h[1]];var o=Math.sqrt(j[0]*j[0]+j[1]*j[1]);if(o>1e-8){j=[j[0]/o,j[1]/o];f=[-j[1],j[0]];var k=myCreateElementSVG("path");k.setAttribute("d","M "+(g[0]-15*j[0]-4*f[0])+" "+(g[1]-15*j[1]-4*f[1])+" L "+(g[0]-3*j[0])+" "+(g[1]-3*j[1])+" L "+(g[0]-15*j[0]+4*f[0])+" "+(g[1]-15*j[1]+4*f[1])+" z");k.setAttribute("stroke-width",markerstrokewidth);k.setAttribute("stroke",stroke);k.setAttribute("fill",stroke);k.setAttribute("stroke-opacity",strokeopacity);k.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(k);}}function chopZ(g){var f=g.indexOf(".");if(f==-1){return g;}for(var h=g.length-1;h>f&&g.charAt(h)=="0";h--){}if(h==f){h--;}return g.slice(0,h+1);}function grid(g,f){axes(g,f,null,g,f);}function noaxes(){if(!initialized){initPicture();}}function axes(dx,dy,labels,gdx,gdy){var x,y,ldx,ldy,lx,ly,lxp,lyp,pnode,st;if(!initialized){initPicture();}if(typeof dx=="string"){labels=dx;dx=null;}if(typeof dy=="string"){gdx=dy;dy=null;}if(xscl!=null){dx=xscl;gdx=xscl;labels=dx;}if(yscl!=null){dy=yscl;gdy=yscl;}if(xtick!=null){dx=xtick;}if(ytick!=null){dy=ytick;}dx=(dx==null?xunitlength:dx*xunitlength);dy=(dy==null?dx:dy*yunitlength);fontsize=Math.min(dx/2,dy/2,16);ticklength=fontsize/4;if(xgrid!=null){gdx=xgrid;}if(ygrid!=null){gdy=ygrid;}if(gdx!=null){gdx=(typeof gdx=="string"?dx:gdx*xunitlength);gdy=(gdy==null?dy:gdy*yunitlength);pnode=myCreateElementSVG("path");st="";for(x=origin[0];x0;x=x-gdx){st+=" M"+x+",0 "+x+","+height;}for(y=height-origin[1];y0;y=y-gdy){st+=" M0,"+y+" "+width+","+y;}pnode.setAttribute("d",st);pnode.setAttribute("stroke-width",0.5);pnode.setAttribute("stroke",gridstroke);pnode.setAttribute("fill",fill);svgpicture.appendChild(pnode);}pnode=myCreateElementSVG("path");st="M0,"+(height-origin[1])+" "+width+","+(height-origin[1])+" M"+origin[0]+",0 "+origin[0]+","+height;for(x=origin[0]+dx;x0;x=x-dx){st+=" M"+x+","+(height-origin[1]+ticklength)+" "+x+","+(height-origin[1]-ticklength);}for(y=height-origin[1]+dy;y0;y=y-dy){st+=" M"+(origin[0]+ticklength)+","+y+" "+(origin[0]-ticklength)+","+y;}if(labels!=null){with(Math){ldx=dx/xunitlength;ldy=dy/yunitlength;lx=(xmin>0||xmax<0?xmin:0);ly=(ymin>0||ymax<0?ymin:0);lxp=(ly==0?"below":"above");lyp=(lx==0?"left":"right");var ddx=floor(1.1-log(ldx)/log(10))+1;var ddy=floor(1.1-log(ldy)/log(10))+1;for(x=ldx;x<=xmax;x=x+ldx){text([x,ly],chopZ(x.toFixed(ddx)),lxp);}for(x=-ldx;xmin<=x;x=x-ldx){text([x,ly],chopZ(x.toFixed(ddx)),lxp);}for(y=ldy;y<=ymax;y=y+ldy){text([lx,y],chopZ(y.toFixed(ddy)),lyp);}for(y=-ldy;ymin<=y;y=y-ldy){text([lx,y],chopZ(y.toFixed(ddy)),lyp);}}}fontsize=defaultfontsize;pnode.setAttribute("d",st);pnode.setAttribute("stroke-width",0.5);pnode.setAttribute("stroke",axesstroke);pnode.setAttribute("fill",fill);pnode.setAttribute("stroke-opacity",strokeopacity);pnode.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(pnode);}function mathjs(h){h=h.replace(/\s/g,"");if(h.indexOf("^-1")!=-1){h=h.replace(/sin\^-1/g,"arcsin");h=h.replace(/cos\^-1/g,"arccos");h=h.replace(/tan\^-1/g,"arctan");h=h.replace(/sec\^-1/g,"arcsec");h=h.replace(/csc\^-1/g,"arccsc");h=h.replace(/cot\^-1/g,"arccot");h=h.replace(/sinh\^-1/g,"arcsinh");h=h.replace(/cosh\^-1/g,"arccosh");h=h.replace(/tanh\^-1/g,"arctanh");h=h.replace(/sech\^-1/g,"arcsech");h=h.replace(/csch\^-1/g,"arccsch");h=h.replace(/coth\^-1/g,"arccoth");}h=h.replace(/^e$/g,"(Math.E)");h=h.replace(/^e([^a-zA-Z])/g,"(Math.E)$1");h=h.replace(/([^a-zA-Z])e/g,"$1(Math.E)");h=h.replace(/([0-9])([\(a-zA-Z])/g,"$1*$2");h=h.replace(/\)([\(0-9a-zA-Z])/g,")*$1");var l,g,f,m,o;while((l=h.indexOf("^"))!=-1){if(l==0){return"Error: missing argument";}g=l-1;m=h.charAt(g);if(m>="0"&&m<="9"){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}if(m=="."){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}}}else{if(m==")"){o=1;g--;while(g>=0&&o>0){m=h.charAt(g);if(m=="("){o--;}else{if(m==")"){o++;}}g--;}while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){g--;while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{return"Error: incorrect syntax in "+h+" at position "+g;}}}if(l==h.length-1){return"Error: missing argument";}f=l+1;m=h.charAt(f);if(m>="0"&&m<="9"||m=="-"){f++;while(f="0"&&m<="9"){f++;}if(m=="."){f++;while(f="0"&&m<="9"){f++;}}}else{if(m=="("){o=1;f++;while(f0){m=h.charAt(f);if(m=="("){o++;}else{if(m==")"){o--;}}f++;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){f++;while(f="a"&&m<="z"||m>="A"&&m<="Z"){f++;}}else{return"Error: incorrect syntax in "+h+" at position "+f;}}}h=h.slice(0,g+1)+"Math.pow("+h.slice(g+1,l)+","+h.slice(l+1,f)+")"+h.slice(f);}while((l=h.indexOf("!"))!=-1){if(l==0){return"Error: missing argument";}g=l-1;m=h.charAt(g);if(m>="0"&&m<="9"){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}if(m=="."){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}}}else{if(m==")"){o=1;g--;while(g>=0&&o>0){m=h.charAt(g);if(m=="("){o--;}else{if(m==")"){o++;}}g--;}while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){g--;while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{return"Error: incorrect syntax in "+h+" at position "+g;}}}h=h.slice(0,g+1)+"factorial("+h.slice(g+1,l)+")"+h.slice(l+1);}return h;}function plot(fun,x_min,x_max,points,id,endpts){var pth=[];var f=function(x){return x;},g=fun;var name=null;if(typeof fun=="string"){eval("g = function(x){ with(Math) return "+mathjs(fun)+" }");}else{if(typeof fun=="object"){eval("f = function(t){ with(Math) return "+mathjs(fun[0])+" }");eval("g = function(t){ with(Math) return "+mathjs(fun[1])+" }");}}if(typeof x_min=="string"){name=x_min;x_min=xmin;}else{name=id;}var min=(x_min==null?xmin:x_min);var max=(x_max==null?xmax:x_max);var inc=max-min-0.000001*(max-min);inc=(points==null?inc/200:inc/points);var gt;for(var t=min;t<=max;t+=inc){gt=g(t);if(!(isNaN(gt)||Math.abs(gt)=="Infinity")){pth[pth.length]=[f(t),gt];}}path(pth,name,null,endpts);return p;}function slopefield(fun,dx,dy){var g=fun;if(typeof fun=="string"){eval("g = function(x,y){ with(Math) return "+mathjs(fun)+" }");}var gxy,x,y,u,v,dz;if(dx==null){dx=1;}if(dy==null){dy=1;}dz=Math.sqrt(dx*dx+dy*dy)/6;var x_min=Math.ceil(xmin/dx);var y_min=Math.ceil(ymin/dy);for(x=x_min;x<=xmax;x+=dx){for(y=y_min;y<=ymax;y+=dy){gxy=g(x,y);if(!isNaN(gxy)){if(Math.abs(gxy)=="Infinity"){u=0;v=dz;}else{u=dz/Math.sqrt(1+gxy*gxy);v=gxy*u;}line([x-u,y-v],[x+u,y+v]);}}}}function show_props(h){var f="";for(var g=0;g\nResult:     \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n
';function generic(){if(translateOnLoad){var g=document.getElementById("processasciimathinmoodle");if(g!=null){dsvglocation=g.className;}if(g!=null||!checkforprocessasciimathinmoodle){if(translateLaTeX){LMtranslate();}if(translateASCIIMath){translate();}if(translateASCIIsvg){drawPictures();}}var f=getElementsByClass(document,"div","ASCIIMathCalculator");if(f.length>0){initASCIIMathCalculators(f);}}}if(typeof window.addEventListener!="undefined"){window.addEventListener("load",generic,false);}else{if(typeof document.addEventListener!="undefined"){document.addEventListener("load",generic,false);}else{if(typeof window.attachEvent!="undefined"){window.attachEvent("onload",generic);}else{if(typeof window.onload=="function"){var existing=onload;window.onload=function(){existing();generic();};}else{window.onload=generic;}}}} \ No newline at end of file +var mathcolor="blue";var mathfontsize="1em";var mathfontfamily="serif";var automathrecognize=false;var checkForMathML=true;var notifyIfNoMathML=true;var alertIfNoMathML=false;var translateOnLoad=true;var translateLaTeX=false;var translateLaTeXformatting=false;var translateASCIIMath=true;var translateASCIIsvg=true;var avoidinnerHTML=false;var displaystyle=true;var showasciiformulaonhover=true;var decimalsign=".";var AMdelimiter1="`",AMescape1="\\\\`";var AMdocumentId="wikitext";var checkforprocessasciimathinmoodle=false;var dsvglocation="";var isIE=document.createElementNS==null;if(document.getElementById==null){alert("This webpage requires a recent browser such as\nMozilla/Netscape 7+ or Internet Explorer 6+MathPlayer");}function AMcreateElementXHTML(f){if(isIE){return document.createElement(f);}else{return document.createElementNS("http://www.w3.org/1999/xhtml",f);}}function AMnoMathMLNote(){var g=AMcreateElementXHTML("h3");g.setAttribute("align","center");g.appendChild(AMcreateElementXHTML("p"));g.appendChild(document.createTextNode("To view the "));var f=AMcreateElementXHTML("a");f.appendChild(document.createTextNode("ASCIIMathML"));f.setAttribute("href","http://www.chapman.edu/~jipsen/asciimath.html");g.appendChild(f);g.appendChild(document.createTextNode(" notation use Internet Explorer 6+"));f=AMcreateElementXHTML("a");f.appendChild(document.createTextNode("MathPlayer"));f.setAttribute("href","http://www.dessci.com/en/products/mathplayer/download.htm");g.appendChild(f);g.appendChild(document.createTextNode(" or Netscape/Mozilla/Firefox"));g.appendChild(AMcreateElementXHTML("p"));return g;}function AMisMathMLavailable(){if(navigator.appName.slice(0,8)=="Netscape"){if(navigator.appVersion.slice(0,1)>="5"){return null;}else{return AMnoMathMLNote();}}else{if(navigator.appName.slice(0,9)=="Microsoft"){try{var g=new ActiveXObject("MathPlayer.Factory.1");return null;}catch(f){return AMnoMathMLNote();}}else{return AMnoMathMLNote();}}}var AMcal=[61237,8492,61238,61239,8496,8497,61240,8459,8464,61241,61242,8466,8499,61243,61244,61245,61246,8475,61247,61248,61249,61250,61251,61252,61253,61254];var AMfrk=[61277,61278,8493,61279,61280,61281,61282,8460,8465,61283,61284,61285,61286,61287,61288,61289,61290,8476,61291,61292,61293,61294,61295,61296,61297,8488];var AMbbb=[61324,61325,8450,61326,61327,61328,61329,8461,61330,61331,61332,61333,61334,8469,61335,8473,8474,8477,61336,61337,61338,61339,61340,61341,61342,8484];var CONST=0,UNARY=1,BINARY=2,INFIX=3,LEFTBRACKET=4,RIGHTBRACKET=5,SPACE=6,UNDEROVER=7,DEFINITION=8,LEFTRIGHT=9,TEXT=10;var AMsqrt={input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:UNARY},AMroot={input:"root",tag:"mroot",output:"root",tex:null,ttype:BINARY},AMfrac={input:"frac",tag:"mfrac",output:"/",tex:null,ttype:BINARY},AMdiv={input:"/",tag:"mfrac",output:"/",tex:null,ttype:INFIX},AMover={input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:BINARY},AMsub={input:"_",tag:"msub",output:"_",tex:null,ttype:INFIX},AMsup={input:"^",tag:"msup",output:"^",tex:null,ttype:INFIX},AMtext={input:"text",tag:"mtext",output:"text",tex:null,ttype:TEXT},AMmbox={input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:TEXT},AMquote={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:TEXT};var AMsymbols=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:CONST},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:CONST},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:CONST},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:CONST},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:CONST},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:CONST},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:CONST},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:CONST},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:CONST},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:CONST},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:CONST},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:CONST},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:CONST},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:CONST},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:CONST},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:CONST},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:CONST},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:CONST},{input:"phi",tag:"mi",output:"\u03C6",tex:null,ttype:CONST},{input:"varphi",tag:"mi",output:"\u03D5",tex:null,ttype:CONST},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:CONST},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:CONST},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:CONST},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:CONST},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:CONST},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:CONST},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:CONST},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:CONST},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:CONST},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:CONST},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:CONST},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:CONST},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:CONST},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:CONST},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:CONST},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:CONST},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:CONST},{input:"**",tag:"mo",output:"\u22C6",tex:"star",ttype:CONST},{input:"//",tag:"mo",output:"/",tex:null,ttype:CONST},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:CONST},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:CONST},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:CONST},{input:"-:",tag:"mo",output:"\u00F7",tex:"divide",ttype:CONST},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:CONST},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:CONST},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:CONST},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:CONST},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:UNDEROVER},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:UNDEROVER},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:CONST},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:UNDEROVER},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:CONST},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:UNDEROVER},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:CONST},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:UNDEROVER},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:CONST},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:UNDEROVER},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:CONST},{input:":=",tag:"mo",output:":=",tex:null,ttype:CONST},{input:"lt",tag:"mo",output:"<",tex:null,ttype:CONST},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:CONST},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:CONST},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:CONST},{input:"geq",tag:"mo",output:"\u2265",tex:null,ttype:CONST},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:CONST},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:CONST},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:CONST},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:CONST},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:CONST},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:CONST},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:CONST},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:CONST},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:CONST},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:CONST},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:CONST},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:CONST},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:CONST},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:CONST},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:CONST},{input:"and",tag:"mtext",output:"and",tex:null,ttype:SPACE},{input:"or",tag:"mtext",output:"or",tex:null,ttype:SPACE},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:CONST},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:CONST},{input:"if",tag:"mo",output:"if",tex:null,ttype:SPACE},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:CONST},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:CONST},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:CONST},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:CONST},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:CONST},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:CONST},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:CONST},{input:"(",tag:"mo",output:"(",tex:null,ttype:LEFTBRACKET},{input:")",tag:"mo",output:")",tex:null,ttype:RIGHTBRACKET},{input:"[",tag:"mo",output:"[",tex:null,ttype:LEFTBRACKET},{input:"]",tag:"mo",output:"]",tex:null,ttype:RIGHTBRACKET},{input:"{",tag:"mo",output:"{",tex:null,ttype:LEFTBRACKET},{input:"}",tag:"mo",output:"}",tex:null,ttype:RIGHTBRACKET},{input:"|",tag:"mo",output:"|",tex:null,ttype:LEFTRIGHT},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:LEFTBRACKET},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:RIGHTBRACKET},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:LEFTBRACKET},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:RIGHTBRACKET},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:LEFTBRACKET,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:RIGHTBRACKET,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:CONST},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:DEFINITION},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:DEFINITION},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:DEFINITION},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:DEFINITION},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:CONST},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:CONST},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:CONST},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:CONST},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:CONST},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:CONST},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:CONST},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:CONST},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:CONST},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:CONST},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:CONST},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:CONST},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:CONST},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:CONST},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:CONST},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:CONST},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:CONST},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:CONST},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:CONST},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:CONST},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:CONST},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:CONST},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:CONST},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:CONST},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:CONST},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:CONST},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:CONST},{input:"f",tag:"mi",output:"f",tex:null,ttype:UNARY,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:UNARY,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:UNDEROVER},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:UNDEROVER},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:UNARY,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:UNARY,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:UNARY,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:UNARY,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:UNARY,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:UNARY,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:UNARY,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:UNARY,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:UNARY,func:true},{input:"log",tag:"mo",output:"log",tex:null,ttype:UNARY,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:UNARY,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:UNARY,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:CONST},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:CONST},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:UNARY,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:UNARY,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:CONST},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:CONST},{input:"min",tag:"mo",output:"min",tex:null,ttype:UNDEROVER},{input:"max",tag:"mo",output:"max",tex:null,ttype:UNDEROVER},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:CONST},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:CONST},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:CONST},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:CONST},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:CONST},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:CONST},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:CONST},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:CONST},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:CONST},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:CONST},AMsqrt,AMroot,AMfrac,AMdiv,AMover,AMsub,AMsup,{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:UNARY,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:UNARY,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:UNARY,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:UNARY,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:UNARY,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:UNARY,acc:true},AMtext,AMmbox,AMquote,{input:"bb",tag:"mstyle",atname:"fontweight",atval:"bold",output:"bb",tex:null,ttype:UNARY},{input:"mathbf",tag:"mstyle",atname:"fontweight",atval:"bold",output:"mathbf",tex:null,ttype:UNARY},{input:"sf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"sf",tex:null,ttype:UNARY},{input:"mathsf",tag:"mstyle",atname:"fontfamily",atval:"sans-serif",output:"mathsf",tex:null,ttype:UNARY},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:UNARY,codes:AMbbb},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:UNARY,codes:AMbbb},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:UNARY,codes:AMcal},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:UNARY,codes:AMcal},{input:"tt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"tt",tex:null,ttype:UNARY},{input:"mathtt",tag:"mstyle",atname:"fontfamily",atval:"monospace",output:"mathtt",tex:null,ttype:UNARY},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:UNARY,codes:AMfrk},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:UNARY,codes:AMfrk}];function compareNames(g,f){if(g.input>f.input){return 1;}else{return -1;}}var AMnames=[];function AMinitSymbols(){var g=[],f;for(f=0;f>1;if(g[f]=AMnames[f];}AMpreviousSymbol=AMcurrentSymbol;if(m!=""){AMcurrentSymbol=AMsymbols[l].ttype;return AMsymbols[l];}AMcurrentSymbol=CONST;f=1;v=q.slice(0,1);var r=true;while("0"<=v&&v<="9"&&f<=q.length){v=q.slice(f,f+1);f++;}if(v==decimalsign){v=q.slice(f,f+1);if("0"<=v&&v<="9"){r=false;f++;while("0"<=v&&v<="9"&&f<=q.length){v=q.slice(f,f+1);f++;}}}if((r&&f>1)||f>2){v=q.slice(0,f-1);s="mn";}else{f=2;v=q.slice(0,1);s=(("A">v||v>"Z")&&("a">v||v>"z")?"mo":"mi");}if(v=="-"&&AMpreviousSymbol==INFIX){AMcurrentSymbol=INFIX;return{input:v,tag:s,output:v,ttype:UNARY,func:true};}return{input:v,tag:s,output:v,ttype:CONST};}function AMremoveBrackets(g){var f;if(g.nodeName=="mrow"){f=g.firstChild.firstChild.nodeValue;if(f=="("||f=="["||f=="{"){g.removeChild(g.firstChild);}}if(g.nodeName=="mrow"){f=g.lastChild.firstChild.nodeValue;if(f==")"||f=="]"||f=="}"){g.removeChild(g.lastChild);}}}var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol;function AMparseSexpr(o){var h,g,s,l,r,m=document.createDocumentFragment();o=AMremoveCharsAndBlanks(o,0);h=AMgetSymbol(o);if(h==null||h.ttype==RIGHTBRACKET&&AMnestingDepth>0){return[null,o];}if(h.ttype==DEFINITION){o=h.output+AMremoveCharsAndBlanks(o,h.input.length);h=AMgetSymbol(o);}switch(h.ttype){case UNDEROVER:case CONST:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];case LEFTBRACKET:AMnestingDepth++;o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseExpr(o,true);AMnestingDepth--;if(typeof h.invisible=="boolean"&&h.invisible){g=AMcreateMmlNode("mrow",s[0]);}else{g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);g.appendChild(s[0]);}return[g,s[1]];case TEXT:if(h!=AMquote){o=AMremoveCharsAndBlanks(o,h.input.length);}if(o.charAt(0)=="{"){l=o.indexOf("}");}else{if(o.charAt(0)=="("){l=o.indexOf(")");}else{if(o.charAt(0)=="["){l=o.indexOf("]");}else{if(h==AMquote){l=o.slice(1).indexOf('"')+1;}else{l=0;}}}}if(l==-1){l=o.length;}r=o.slice(1,l);if(r.charAt(0)==" "){g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);}m.appendChild(AMcreateMmlNode(h.tag,document.createTextNode(r)));if(r.charAt(r.length-1)==" "){g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);}o=AMremoveCharsAndBlanks(o,l+1);return[AMcreateMmlNode("mrow",m),o];case UNARY:o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseSexpr(o);if(s[0]==null){return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}if(typeof h.func=="boolean"&&h.func){r=o.charAt(0);if(r=="^"||r=="_"||r=="/"||r=="|"||r==","){return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}else{g=AMcreateMmlNode("mrow",AMcreateMmlNode(h.tag,document.createTextNode(h.output)));g.appendChild(s[0]);return[g,s[1]];}}AMremoveBrackets(s[0]);if(h.input=="sqrt"){return[AMcreateMmlNode(h.tag,s[0]),s[1]];}else{if(typeof h.acc=="boolean"&&h.acc){g=AMcreateMmlNode(h.tag,s[0]);g.appendChild(AMcreateMmlNode("mo",document.createTextNode(h.output)));return[g,s[1]];}else{if(!isIE&&typeof h.codes!="undefined"){for(l=0;l64&&r.charCodeAt(k)<91){q=q+String.fromCharCode(h.codes[r.charCodeAt(k)-65]);}else{q=q+r.charAt(k);}}if(s[0].nodeName=="mi"){s[0]=AMcreateElementMathML("mo").appendChild(document.createTextNode(q));}else{s[0].replaceChild(AMcreateElementMathML("mo").appendChild(document.createTextNode(q)),s[0].childNodes[l]);}}}}g=AMcreateMmlNode(h.tag,s[0]);g.setAttribute(h.atname,h.atval);return[g,s[1]];}}case BINARY:o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseSexpr(o);if(s[0]==null){return[AMcreateMmlNode("mo",document.createTextNode(h.input)),o];}AMremoveBrackets(s[0]);var f=AMparseSexpr(s[1]);if(f[0]==null){return[AMcreateMmlNode("mo",document.createTextNode(h.input)),o];}AMremoveBrackets(f[0]);if(h.input=="root"||h.input=="stackrel"){m.appendChild(f[0]);}m.appendChild(s[0]);if(h.input=="frac"){m.appendChild(f[0]);}return[AMcreateMmlNode(h.tag,m),f[1]];case INFIX:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode("mo",document.createTextNode(h.output)),o];case SPACE:o=AMremoveCharsAndBlanks(o,h.input.length);g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);m.appendChild(AMcreateMmlNode(h.tag,document.createTextNode(h.output)));g=AMcreateElementMathML("mspace");g.setAttribute("width","1ex");m.appendChild(g);return[AMcreateMmlNode("mrow",m),o];case LEFTRIGHT:AMnestingDepth++;o=AMremoveCharsAndBlanks(o,h.input.length);s=AMparseExpr(o,false);AMnestingDepth--;var r="";if(s[0].lastChild!=null){r=s[0].lastChild.firstChild.nodeValue;}if(r=="|"){g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);g.appendChild(s[0]);return[g,s[1]];}else{g=AMcreateMmlNode("mo",document.createTextNode(h.output));g=AMcreateMmlNode("mrow",g);return[g,o];}default:o=AMremoveCharsAndBlanks(o,h.input.length);return[AMcreateMmlNode(h.tag,document.createTextNode(h.output)),o];}}function AMparseIexpr(m){var k,o,l,j,f,h;m=AMremoveCharsAndBlanks(m,0);o=AMgetSymbol(m);f=AMparseSexpr(m);j=f[0];m=f[1];k=AMgetSymbol(m);if(k.ttype==INFIX&&k.input!="/"){m=AMremoveCharsAndBlanks(m,k.input.length);f=AMparseSexpr(m);if(f[0]==null){f[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));}else{AMremoveBrackets(f[0]);}m=f[1];if(k.input=="_"){l=AMgetSymbol(m);h=(o.ttype==UNDEROVER);if(l.input=="^"){m=AMremoveCharsAndBlanks(m,l.input.length);var g=AMparseSexpr(m);AMremoveBrackets(g[0]);m=g[1];j=AMcreateMmlNode((h?"munderover":"msubsup"),j);j.appendChild(f[0]);j.appendChild(g[0]);j=AMcreateMmlNode("mrow",j);}else{j=AMcreateMmlNode((h?"munder":"msub"),j);j.appendChild(f[0]);}}else{j=AMcreateMmlNode(k.tag,j);j.appendChild(f[0]);}}return[j,m];}function AMparseExpr(v,s){var B,w,o,F,J=[],q=document.createDocumentFragment();do{v=AMremoveCharsAndBlanks(v,0);o=AMparseIexpr(v);w=o[0];v=o[1];B=AMgetSymbol(v);if(B.ttype==INFIX&&B.input=="/"){v=AMremoveCharsAndBlanks(v,B.input.length);o=AMparseIexpr(v);if(o[0]==null){o[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));}else{AMremoveBrackets(o[0]);}v=o[1];AMremoveBrackets(w);w=AMcreateMmlNode(B.tag,w);w.appendChild(o[0]);q.appendChild(w);B=AMgetSymbol(v);}else{if(w!=undefined){q.appendChild(w);}}}while((B.ttype!=RIGHTBRACKET&&(B.ttype!=LEFTRIGHT||s)||AMnestingDepth==0)&&B!=null&&B.output!="");if(B.ttype==RIGHTBRACKET||B.ttype==LEFTRIGHT){var G=q.childNodes.length;if(G>0&&q.childNodes[G-1].nodeName=="mrow"&&G>1&&q.childNodes[G-2].nodeName=="mo"&&q.childNodes[G-2].firstChild.nodeValue==","){var I=q.childNodes[G-1].lastChild.firstChild.nodeValue;if(I==")"||I=="]"){var g=q.childNodes[G-1].firstChild.firstChild.nodeValue;if(g=="("&&I==")"&&B.output!="}"||g=="["&&I=="]"){var h=[];var D=true;var z=q.childNodes.length;for(F=0;D&&F1){D=h[F].length==h[F-2].length;}}if(D){var l,f,r,A,H=document.createDocumentFragment();for(F=0;F2){q.removeChild(q.firstChild);q.removeChild(q.firstChild);}H.appendChild(AMcreateMmlNode("mtr",l));}w=AMcreateMmlNode("mtable",H);if(typeof B.invisible=="boolean"&&B.invisible){w.setAttribute("columnalign","left");}q.replaceChild(w,q.firstChild);}}}}v=AMremoveCharsAndBlanks(v,B.input.length);if(typeof B.invisible!="boolean"||!B.invisible){w=AMcreateMmlNode("mo",document.createTextNode(B.output));q.appendChild(w);}}return[q,v];}function AMparseMath(j){var f,h=AMcreateElementMathML("mstyle");if(mathcolor!=""){h.setAttribute("mathcolor",mathcolor);}if(displaystyle){h.setAttribute("displaystyle","true");}if(mathfontfamily!=""){h.setAttribute("fontfamily",mathfontfamily);}AMnestingDepth=0;h.appendChild(AMparseExpr(j.replace(/^\s+/g,""),false)[0]);h=AMcreateMmlNode("math",h);if(showasciiformulaonhover){h.setAttribute("title",j.replace(/\s+/g," "));}var g=AMcreateElementXHTML("span");g.style.fontSize=mathfontsize;if(mathfontfamily!=""){g.style.fontFamily=mathfontfamily;}g.appendChild(h);return g;}function AMstrarr2docFrag(f,k){var o=document.createDocumentFragment();var m=false;for(var l=0;l,\\|!:;'~]|\\.(?!(?:\x20|$))|"+q+s+f;var v=new RegExp("(^|\\s)((("+k+")\\s?)(("+k+j+")\\s?)+)([,.?]?(?=\\s|$))","g");r=r.replace(v," `$2`$7");var m=r.split(AMdelimiter1);var o=new RegExp("(^|\\s)([b-zB-HJ-Z+*<>]|"+h+q+f+")(\\s|\\n|$)","g");var l=new RegExp("(^|\\s)([a-z]|"+h+q+f+")([,.])","g");for(i=0;i1||q){if(checkForMathML){checkForMathML=false;var h=AMisMathMLavailable();AMnoMathML=h!=null;if(AMnoMathML&¬ifyIfNoMathML){if(alertIfNoMathML){alert("To view the ASCIIMathML notation use Internet Explorer 6 +\nMathPlayer (free from www.dessci.com)\n or Firefox/Mozilla/Netscape");}else{AMbody.insertBefore(h,AMbody.childNodes[0]);}}}if(!AMnoMathML){f=AMstrarr2docFrag(k,g.nodeType==8);var l=f.childNodes.length;g.parentNode.replaceChild(f,g);return l-1;}else{return 0;}}}}else{return 0;}}else{if(g.nodeName!="math"){for(j=0;j="5"){return null;}else{return LMnoMathMLNote();}}else{if(navigator.appName.slice(0,9)=="Microsoft"){try{var g=new ActiveXObject("MathPlayer.Factory.1");return null;}catch(f){return LMnoMathMLNote();}}else{return LMnoMathMLNote();}}}var LMcal=[61237,8492,61238,61239,8496,8497,61240,8459,8464,61241,61242,8466,8499,61243,61244,61245,61246,8475,61247,61248,61249,61250,61251,61252,61253,61254];var LMfrk=[61277,61278,8493,61279,61280,61281,61282,8460,8465,61283,61284,61285,61286,61287,61288,61289,61290,8476,61291,61292,61293,61294,61295,61296,61297,8488];var LMbbb=[61324,61325,8450,61326,61327,61328,61329,8461,61330,61331,61332,61333,61334,8469,61335,8473,8474,8477,61336,61337,61338,61339,61340,61341,61342,8484];var BIG=11,LONG=12,STRETCHY=13,MATRIX=14;var LMsqrt={input:"\\sqrt",tag:"msqrt",output:"sqrt",ttype:UNARY},LMroot={input:"\\root",tag:"mroot",output:"root",ttype:BINARY},LMfrac={input:"\\frac",tag:"mfrac",output:"/",ttype:BINARY},LMover={input:"\\stackrel",tag:"mover",output:"stackrel",ttype:BINARY},LMatop={input:"\\atop",tag:"mfrac",output:"",ttype:INFIX},LMchoose={input:"\\choose",tag:"mfrac",output:"",ttype:INFIX},LMsub={input:"_",tag:"msub",output:"_",ttype:INFIX},LMsup={input:"^",tag:"msup",output:"^",ttype:INFIX},LMtext={input:"\\mathrm",tag:"mtext",output:"text",ttype:TEXT},LMmbox={input:"\\mbox",tag:"mtext",output:"mbox",ttype:TEXT};var LMsymbols=[{input:"\\alpha",tag:"mi",output:"\u03B1",ttype:CONST},{input:"\\beta",tag:"mi",output:"\u03B2",ttype:CONST},{input:"\\gamma",tag:"mi",output:"\u03B3",ttype:CONST},{input:"\\delta",tag:"mi",output:"\u03B4",ttype:CONST},{input:"\\epsilon",tag:"mi",output:"\u03B5",ttype:CONST},{input:"\\varepsilon",tag:"mi",output:"\u025B",ttype:CONST},{input:"\\zeta",tag:"mi",output:"\u03B6",ttype:CONST},{input:"\\eta",tag:"mi",output:"\u03B7",ttype:CONST},{input:"\\theta",tag:"mi",output:"\u03B8",ttype:CONST},{input:"\\vartheta",tag:"mi",output:"\u03D1",ttype:CONST},{input:"\\iota",tag:"mi",output:"\u03B9",ttype:CONST},{input:"\\kappa",tag:"mi",output:"\u03BA",ttype:CONST},{input:"\\lambda",tag:"mi",output:"\u03BB",ttype:CONST},{input:"\\mu",tag:"mi",output:"\u03BC",ttype:CONST},{input:"\\nu",tag:"mi",output:"\u03BD",ttype:CONST},{input:"\\xi",tag:"mi",output:"\u03BE",ttype:CONST},{input:"\\pi",tag:"mi",output:"\u03C0",ttype:CONST},{input:"\\varpi",tag:"mi",output:"\u03D6",ttype:CONST},{input:"\\rho",tag:"mi",output:"\u03C1",ttype:CONST},{input:"\\varrho",tag:"mi",output:"\u03F1",ttype:CONST},{input:"\\varsigma",tag:"mi",output:"\u03C2",ttype:CONST},{input:"\\sigma",tag:"mi",output:"\u03C3",ttype:CONST},{input:"\\tau",tag:"mi",output:"\u03C4",ttype:CONST},{input:"\\upsilon",tag:"mi",output:"\u03C5",ttype:CONST},{input:"\\phi",tag:"mi",output:"\u03C6",ttype:CONST},{input:"\\varphi",tag:"mi",output:"\u03D5",ttype:CONST},{input:"\\chi",tag:"mi",output:"\u03C7",ttype:CONST},{input:"\\psi",tag:"mi",output:"\u03C8",ttype:CONST},{input:"\\omega",tag:"mi",output:"\u03C9",ttype:CONST},{input:"\\Gamma",tag:"mo",output:"\u0393",ttype:CONST},{input:"\\Delta",tag:"mo",output:"\u0394",ttype:CONST},{input:"\\Theta",tag:"mo",output:"\u0398",ttype:CONST},{input:"\\Lambda",tag:"mo",output:"\u039B",ttype:CONST},{input:"\\Xi",tag:"mo",output:"\u039E",ttype:CONST},{input:"\\Pi",tag:"mo",output:"\u03A0",ttype:CONST},{input:"\\Sigma",tag:"mo",output:"\u03A3",ttype:CONST},{input:"\\Upsilon",tag:"mo",output:"\u03A5",ttype:CONST},{input:"\\Phi",tag:"mo",output:"\u03A6",ttype:CONST},{input:"\\Psi",tag:"mo",output:"\u03A8",ttype:CONST},{input:"\\Omega",tag:"mo",output:"\u03A9",ttype:CONST},{input:"\\frac12",tag:"mo",output:"\u00BD",ttype:CONST},{input:"\\frac14",tag:"mo",output:"\u00BC",ttype:CONST},{input:"\\frac34",tag:"mo",output:"\u00BE",ttype:CONST},{input:"\\frac13",tag:"mo",output:"\u2153",ttype:CONST},{input:"\\frac23",tag:"mo",output:"\u2154",ttype:CONST},{input:"\\frac15",tag:"mo",output:"\u2155",ttype:CONST},{input:"\\frac25",tag:"mo",output:"\u2156",ttype:CONST},{input:"\\frac35",tag:"mo",output:"\u2157",ttype:CONST},{input:"\\frac45",tag:"mo",output:"\u2158",ttype:CONST},{input:"\\frac16",tag:"mo",output:"\u2159",ttype:CONST},{input:"\\frac56",tag:"mo",output:"\u215A",ttype:CONST},{input:"\\frac18",tag:"mo",output:"\u215B",ttype:CONST},{input:"\\frac38",tag:"mo",output:"\u215C",ttype:CONST},{input:"\\frac58",tag:"mo",output:"\u215D",ttype:CONST},{input:"\\frac78",tag:"mo",output:"\u215E",ttype:CONST},{input:"\\pm",tag:"mo",output:"\u00B1",ttype:CONST},{input:"\\mp",tag:"mo",output:"\u2213",ttype:CONST},{input:"\\triangleleft",tag:"mo",output:"\u22B2",ttype:CONST},{input:"\\triangleright",tag:"mo",output:"\u22B3",ttype:CONST},{input:"\\cdot",tag:"mo",output:"\u22C5",ttype:CONST},{input:"\\star",tag:"mo",output:"\u22C6",ttype:CONST},{input:"\\ast",tag:"mo",output:"\u002A",ttype:CONST},{input:"\\times",tag:"mo",output:"\u00D7",ttype:CONST},{input:"\\div",tag:"mo",output:"\u00F7",ttype:CONST},{input:"\\circ",tag:"mo",output:"\u2218",ttype:CONST},{input:"\\bullet",tag:"mo",output:"\u2022",ttype:CONST},{input:"\\oplus",tag:"mo",output:"\u2295",ttype:CONST},{input:"\\ominus",tag:"mo",output:"\u2296",ttype:CONST},{input:"\\otimes",tag:"mo",output:"\u2297",ttype:CONST},{input:"\\bigcirc",tag:"mo",output:"\u25CB",ttype:CONST},{input:"\\oslash",tag:"mo",output:"\u2298",ttype:CONST},{input:"\\odot",tag:"mo",output:"\u2299",ttype:CONST},{input:"\\land",tag:"mo",output:"\u2227",ttype:CONST},{input:"\\wedge",tag:"mo",output:"\u2227",ttype:CONST},{input:"\\lor",tag:"mo",output:"\u2228",ttype:CONST},{input:"\\vee",tag:"mo",output:"\u2228",ttype:CONST},{input:"\\cap",tag:"mo",output:"\u2229",ttype:CONST},{input:"\\cup",tag:"mo",output:"\u222A",ttype:CONST},{input:"\\sqcap",tag:"mo",output:"\u2293",ttype:CONST},{input:"\\sqcup",tag:"mo",output:"\u2294",ttype:CONST},{input:"\\uplus",tag:"mo",output:"\u228E",ttype:CONST},{input:"\\amalg",tag:"mo",output:"\u2210",ttype:CONST},{input:"\\bigtriangleup",tag:"mo",output:"\u25B3",ttype:CONST},{input:"\\bigtriangledown",tag:"mo",output:"\u25BD",ttype:CONST},{input:"\\dag",tag:"mo",output:"\u2020",ttype:CONST},{input:"\\dagger",tag:"mo",output:"\u2020",ttype:CONST},{input:"\\ddag",tag:"mo",output:"\u2021",ttype:CONST},{input:"\\ddagger",tag:"mo",output:"\u2021",ttype:CONST},{input:"\\lhd",tag:"mo",output:"\u22B2",ttype:CONST},{input:"\\rhd",tag:"mo",output:"\u22B3",ttype:CONST},{input:"\\unlhd",tag:"mo",output:"\u22B4",ttype:CONST},{input:"\\unrhd",tag:"mo",output:"\u22B5",ttype:CONST},{input:"\\sum",tag:"mo",output:"\u2211",ttype:UNDEROVER},{input:"\\prod",tag:"mo",output:"\u220F",ttype:UNDEROVER},{input:"\\bigcap",tag:"mo",output:"\u22C2",ttype:UNDEROVER},{input:"\\bigcup",tag:"mo",output:"\u22C3",ttype:UNDEROVER},{input:"\\bigwedge",tag:"mo",output:"\u22C0",ttype:UNDEROVER},{input:"\\bigvee",tag:"mo",output:"\u22C1",ttype:UNDEROVER},{input:"\\bigsqcap",tag:"mo",output:"\u2A05",ttype:UNDEROVER},{input:"\\bigsqcup",tag:"mo",output:"\u2A06",ttype:UNDEROVER},{input:"\\coprod",tag:"mo",output:"\u2210",ttype:UNDEROVER},{input:"\\bigoplus",tag:"mo",output:"\u2A01",ttype:UNDEROVER},{input:"\\bigotimes",tag:"mo",output:"\u2A02",ttype:UNDEROVER},{input:"\\bigodot",tag:"mo",output:"\u2A00",ttype:UNDEROVER},{input:"\\biguplus",tag:"mo",output:"\u2A04",ttype:UNDEROVER},{input:"\\int",tag:"mo",output:"\u222B",ttype:CONST},{input:"\\oint",tag:"mo",output:"\u222E",ttype:CONST},{input:":=",tag:"mo",output:":=",ttype:CONST},{input:"\\lt",tag:"mo",output:"<",ttype:CONST},{input:"\\gt",tag:"mo",output:">",ttype:CONST},{input:"\\ne",tag:"mo",output:"\u2260",ttype:CONST},{input:"\\neq",tag:"mo",output:"\u2260",ttype:CONST},{input:"\\le",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\leq",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\leqslant",tag:"mo",output:"\u2264",ttype:CONST},{input:"\\ge",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\geq",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\geqslant",tag:"mo",output:"\u2265",ttype:CONST},{input:"\\equiv",tag:"mo",output:"\u2261",ttype:CONST},{input:"\\ll",tag:"mo",output:"\u226A",ttype:CONST},{input:"\\gg",tag:"mo",output:"\u226B",ttype:CONST},{input:"\\doteq",tag:"mo",output:"\u2250",ttype:CONST},{input:"\\prec",tag:"mo",output:"\u227A",ttype:CONST},{input:"\\succ",tag:"mo",output:"\u227B",ttype:CONST},{input:"\\preceq",tag:"mo",output:"\u227C",ttype:CONST},{input:"\\succeq",tag:"mo",output:"\u227D",ttype:CONST},{input:"\\subset",tag:"mo",output:"\u2282",ttype:CONST},{input:"\\supset",tag:"mo",output:"\u2283",ttype:CONST},{input:"\\subseteq",tag:"mo",output:"\u2286",ttype:CONST},{input:"\\supseteq",tag:"mo",output:"\u2287",ttype:CONST},{input:"\\sqsubset",tag:"mo",output:"\u228F",ttype:CONST},{input:"\\sqsupset",tag:"mo",output:"\u2290",ttype:CONST},{input:"\\sqsubseteq",tag:"mo",output:"\u2291",ttype:CONST},{input:"\\sqsupseteq",tag:"mo",output:"\u2292",ttype:CONST},{input:"\\sim",tag:"mo",output:"\u223C",ttype:CONST},{input:"\\simeq",tag:"mo",output:"\u2243",ttype:CONST},{input:"\\approx",tag:"mo",output:"\u2248",ttype:CONST},{input:"\\cong",tag:"mo",output:"\u2245",ttype:CONST},{input:"\\Join",tag:"mo",output:"\u22C8",ttype:CONST},{input:"\\bowtie",tag:"mo",output:"\u22C8",ttype:CONST},{input:"\\in",tag:"mo",output:"\u2208",ttype:CONST},{input:"\\ni",tag:"mo",output:"\u220B",ttype:CONST},{input:"\\owns",tag:"mo",output:"\u220B",ttype:CONST},{input:"\\propto",tag:"mo",output:"\u221D",ttype:CONST},{input:"\\vdash",tag:"mo",output:"\u22A2",ttype:CONST},{input:"\\dashv",tag:"mo",output:"\u22A3",ttype:CONST},{input:"\\models",tag:"mo",output:"\u22A8",ttype:CONST},{input:"\\perp",tag:"mo",output:"\u22A5",ttype:CONST},{input:"\\smile",tag:"mo",output:"\u2323",ttype:CONST},{input:"\\frown",tag:"mo",output:"\u2322",ttype:CONST},{input:"\\asymp",tag:"mo",output:"\u224D",ttype:CONST},{input:"\\notin",tag:"mo",output:"\u2209",ttype:CONST},{input:"\\begin{eqnarray}",output:"X",ttype:MATRIX,invisible:true},{input:"\\begin{array}",output:"X",ttype:MATRIX,invisible:true},{input:"\\\\",output:"}&{",ttype:DEFINITION},{input:"\\end{eqnarray}",output:"}}",ttype:DEFINITION},{input:"\\end{array}",output:"}}",ttype:DEFINITION},{input:"\\big",tag:"mo",output:"X",atval:"1.2",ieval:"2.2",ttype:BIG},{input:"\\Big",tag:"mo",output:"X",atval:"1.6",ieval:"2.6",ttype:BIG},{input:"\\bigg",tag:"mo",output:"X",atval:"2.2",ieval:"3.2",ttype:BIG},{input:"\\Bigg",tag:"mo",output:"X",atval:"2.9",ieval:"3.9",ttype:BIG},{input:"\\left",tag:"mo",output:"X",ttype:LEFTBRACKET},{input:"\\right",tag:"mo",output:"X",ttype:RIGHTBRACKET},{input:"{",output:"{",ttype:LEFTBRACKET,invisible:true},{input:"}",output:"}",ttype:RIGHTBRACKET,invisible:true},{input:"(",tag:"mo",output:"(",atval:"1",ttype:STRETCHY},{input:"[",tag:"mo",output:"[",atval:"1",ttype:STRETCHY},{input:"\\lbrack",tag:"mo",output:"[",atval:"1",ttype:STRETCHY},{input:"\\{",tag:"mo",output:"{",atval:"1",ttype:STRETCHY},{input:"\\lbrace",tag:"mo",output:"{",atval:"1",ttype:STRETCHY},{input:"\\langle",tag:"mo",output:"\u2329",atval:"1",ttype:STRETCHY},{input:"\\lfloor",tag:"mo",output:"\u230A",atval:"1",ttype:STRETCHY},{input:"\\lceil",tag:"mo",output:"\u2308",atval:"1",ttype:STRETCHY},{input:")",tag:"mo",output:")",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"]",tag:"mo",output:"]",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rbrack",tag:"mo",output:"]",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\}",tag:"mo",output:"}",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rbrace",tag:"mo",output:"}",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rangle",tag:"mo",output:"\u232A",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rfloor",tag:"mo",output:"\u230B",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"\\rceil",tag:"mo",output:"\u2309",rtag:"mi",atval:"1",ttype:STRETCHY},{input:"|",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\|",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"\\vert",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\Vert",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"\\mid",tag:"mo",output:"\u2223",atval:"1",ttype:STRETCHY},{input:"\\parallel",tag:"mo",output:"\u2225",atval:"1",ttype:STRETCHY},{input:"/",tag:"mo",output:"/",atval:"1.01",ttype:STRETCHY},{input:"\\backslash",tag:"mo",output:"\u2216",atval:"1",ttype:STRETCHY},{input:"\\setminus",tag:"mo",output:"\\",ttype:CONST},{input:"\\!",tag:"mspace",atname:"width",atval:"-0.167em",ttype:SPACE},{input:"\\,",tag:"mspace",atname:"width",atval:"0.167em",ttype:SPACE},{input:"\\>",tag:"mspace",atname:"width",atval:"0.222em",ttype:SPACE},{input:"\\:",tag:"mspace",atname:"width",atval:"0.222em",ttype:SPACE},{input:"\\;",tag:"mspace",atname:"width",atval:"0.278em",ttype:SPACE},{input:"~",tag:"mspace",atname:"width",atval:"0.333em",ttype:SPACE},{input:"\\quad",tag:"mspace",atname:"width",atval:"1em",ttype:SPACE},{input:"\\qquad",tag:"mspace",atname:"width",atval:"2em",ttype:SPACE},{input:"\\prime",tag:"mo",output:"\u2032",ttype:CONST},{input:"'",tag:"mo",output:"\u02B9",ttype:CONST},{input:"''",tag:"mo",output:"\u02BA",ttype:CONST},{input:"'''",tag:"mo",output:"\u2034",ttype:CONST},{input:"''''",tag:"mo",output:"\u2057",ttype:CONST},{input:"\\ldots",tag:"mo",output:"\u2026",ttype:CONST},{input:"\\cdots",tag:"mo",output:"\u22EF",ttype:CONST},{input:"\\vdots",tag:"mo",output:"\u22EE",ttype:CONST},{input:"\\ddots",tag:"mo",output:"\u22F1",ttype:CONST},{input:"\\forall",tag:"mo",output:"\u2200",ttype:CONST},{input:"\\exists",tag:"mo",output:"\u2203",ttype:CONST},{input:"\\Re",tag:"mo",output:"\u211C",ttype:CONST},{input:"\\Im",tag:"mo",output:"\u2111",ttype:CONST},{input:"\\aleph",tag:"mo",output:"\u2135",ttype:CONST},{input:"\\hbar",tag:"mo",output:"\u210F",ttype:CONST},{input:"\\ell",tag:"mo",output:"\u2113",ttype:CONST},{input:"\\wp",tag:"mo",output:"\u2118",ttype:CONST},{input:"\\emptyset",tag:"mo",output:"\u2205",ttype:CONST},{input:"\\infty",tag:"mo",output:"\u221E",ttype:CONST},{input:"\\surd",tag:"mo",output:"\\sqrt{}",ttype:DEFINITION},{input:"\\partial",tag:"mo",output:"\u2202",ttype:CONST},{input:"\\nabla",tag:"mo",output:"\u2207",ttype:CONST},{input:"\\triangle",tag:"mo",output:"\u25B3",ttype:CONST},{input:"\\therefore",tag:"mo",output:"\u2234",ttype:CONST},{input:"\\angle",tag:"mo",output:"\u2220",ttype:CONST},{input:"\\diamond",tag:"mo",output:"\u22C4",ttype:CONST},{input:"\\Diamond",tag:"mo",output:"\u25C7",ttype:CONST},{input:"\\neg",tag:"mo",output:"\u00AC",ttype:CONST},{input:"\\lnot",tag:"mo",output:"\u00AC",ttype:CONST},{input:"\\bot",tag:"mo",output:"\u22A5",ttype:CONST},{input:"\\top",tag:"mo",output:"\u22A4",ttype:CONST},{input:"\\square",tag:"mo",output:"\u25AB",ttype:CONST},{input:"\\Box",tag:"mo",output:"\u25A1",ttype:CONST},{input:"\\wr",tag:"mo",output:"\u2240",ttype:CONST},{input:"\\arccos",tag:"mi",output:"arccos",ttype:UNARY,func:true},{input:"\\arcsin",tag:"mi",output:"arcsin",ttype:UNARY,func:true},{input:"\\arctan",tag:"mi",output:"arctan",ttype:UNARY,func:true},{input:"\\arg",tag:"mi",output:"arg",ttype:UNARY,func:true},{input:"\\cos",tag:"mi",output:"cos",ttype:UNARY,func:true},{input:"\\cosh",tag:"mi",output:"cosh",ttype:UNARY,func:true},{input:"\\cot",tag:"mi",output:"cot",ttype:UNARY,func:true},{input:"\\coth",tag:"mi",output:"coth",ttype:UNARY,func:true},{input:"\\csc",tag:"mi",output:"csc",ttype:UNARY,func:true},{input:"\\deg",tag:"mi",output:"deg",ttype:UNARY,func:true},{input:"\\det",tag:"mi",output:"det",ttype:UNARY,func:true},{input:"\\dim",tag:"mi",output:"dim",ttype:UNARY,func:true},{input:"\\exp",tag:"mi",output:"exp",ttype:UNARY,func:true},{input:"\\gcd",tag:"mi",output:"gcd",ttype:UNARY,func:true},{input:"\\hom",tag:"mi",output:"hom",ttype:UNARY,func:true},{input:"\\inf",tag:"mo",output:"inf",ttype:UNDEROVER},{input:"\\ker",tag:"mi",output:"ker",ttype:UNARY,func:true},{input:"\\lg",tag:"mi",output:"lg",ttype:UNARY,func:true},{input:"\\lim",tag:"mo",output:"lim",ttype:UNDEROVER},{input:"\\liminf",tag:"mo",output:"liminf",ttype:UNDEROVER},{input:"\\limsup",tag:"mo",output:"limsup",ttype:UNDEROVER},{input:"\\ln",tag:"mi",output:"ln",ttype:UNARY,func:true},{input:"\\log",tag:"mi",output:"log",ttype:UNARY,func:true},{input:"\\max",tag:"mo",output:"max",ttype:UNDEROVER},{input:"\\min",tag:"mo",output:"min",ttype:UNDEROVER},{input:"\\Pr",tag:"mi",output:"Pr",ttype:UNARY,func:true},{input:"\\sec",tag:"mi",output:"sec",ttype:UNARY,func:true},{input:"\\sin",tag:"mi",output:"sin",ttype:UNARY,func:true},{input:"\\sinh",tag:"mi",output:"sinh",ttype:UNARY,func:true},{input:"\\sup",tag:"mo",output:"sup",ttype:UNDEROVER},{input:"\\tan",tag:"mi",output:"tan",ttype:UNARY,func:true},{input:"\\tanh",tag:"mi",output:"tanh",ttype:UNARY,func:true},{input:"\\gets",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\leftarrow",tag:"mo",output:"\u2190",ttype:CONST},{input:"\\to",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\rightarrow",tag:"mo",output:"\u2192",ttype:CONST},{input:"\\leftrightarrow",tag:"mo",output:"\u2194",ttype:CONST},{input:"\\uparrow",tag:"mo",output:"\u2191",ttype:CONST},{input:"\\downarrow",tag:"mo",output:"\u2193",ttype:CONST},{input:"\\updownarrow",tag:"mo",output:"\u2195",ttype:CONST},{input:"\\Leftarrow",tag:"mo",output:"\u21D0",ttype:CONST},{input:"\\Rightarrow",tag:"mo",output:"\u21D2",ttype:CONST},{input:"\\Leftrightarrow",tag:"mo",output:"\u21D4",ttype:CONST},{input:"\\iff",tag:"mo",output:"~\\Longleftrightarrow~",ttype:DEFINITION},{input:"\\Uparrow",tag:"mo",output:"\u21D1",ttype:CONST},{input:"\\Downarrow",tag:"mo",output:"\u21D3",ttype:CONST},{input:"\\Updownarrow",tag:"mo",output:"\u21D5",ttype:CONST},{input:"\\mapsto",tag:"mo",output:"\u21A6",ttype:CONST},{input:"\\longleftarrow",tag:"mo",output:"\u2190",ttype:LONG},{input:"\\longrightarrow",tag:"mo",output:"\u2192",ttype:LONG},{input:"\\longleftrightarrow",tag:"mo",output:"\u2194",ttype:LONG},{input:"\\Longleftarrow",tag:"mo",output:"\u21D0",ttype:LONG},{input:"\\Longrightarrow",tag:"mo",output:"\u21D2",ttype:LONG},{input:"\\Longleftrightarrow",tag:"mo",output:"\u21D4",ttype:LONG},{input:"\\longmapsto",tag:"mo",output:"\u21A6",ttype:CONST},LMsqrt,LMroot,LMfrac,LMover,LMsub,LMsup,LMtext,LMmbox,LMatop,LMchoose,{input:"\\acute",tag:"mover",output:"\u00B4",ttype:UNARY,acc:true},{input:"\\grave",tag:"mover",output:"\u0060",ttype:UNARY,acc:true},{input:"\\breve",tag:"mover",output:"\u02D8",ttype:UNARY,acc:true},{input:"\\check",tag:"mover",output:"\u02C7",ttype:UNARY,acc:true},{input:"\\dot",tag:"mover",output:".",ttype:UNARY,acc:true},{input:"\\ddot",tag:"mover",output:"..",ttype:UNARY,acc:true},{input:"\\mathring",tag:"mover",output:"\u00B0",ttype:UNARY,acc:true},{input:"\\vec",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overrightarrow",tag:"mover",output:"\u20D7",ttype:UNARY,acc:true},{input:"\\overleftarrow",tag:"mover",output:"\u20D6",ttype:UNARY,acc:true},{input:"\\hat",tag:"mover",output:"\u005E",ttype:UNARY,acc:true},{input:"\\widehat",tag:"mover",output:"\u0302",ttype:UNARY,acc:true},{input:"\\tilde",tag:"mover",output:"~",ttype:UNARY,acc:true},{input:"\\widetilde",tag:"mover",output:"\u02DC",ttype:UNARY,acc:true},{input:"\\bar",tag:"mover",output:"\u203E",ttype:UNARY,acc:true},{input:"\\overbrace",tag:"mover",output:"\u23B4",ttype:UNARY,acc:true},{input:"\\overline",tag:"mover",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\underbrace",tag:"munder",output:"\u23B5",ttype:UNARY,acc:true},{input:"\\underline",tag:"munder",output:"\u00AF",ttype:UNARY,acc:true},{input:"\\displaystyle",tag:"mstyle",atname:"displaystyle",atval:"true",ttype:UNARY},{input:"\\textstyle",tag:"mstyle",atname:"displaystyle",atval:"false",ttype:UNARY},{input:"\\scriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"1",ttype:UNARY},{input:"\\scriptscriptstyle",tag:"mstyle",atname:"scriptlevel",atval:"2",ttype:UNARY},{input:"\\textrm",tag:"mstyle",output:"\\mathrm",ttype:DEFINITION},{input:"\\mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\textbf",tag:"mstyle",atname:"mathvariant",atval:"bold",ttype:UNARY},{input:"\\mathit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\textit",tag:"mstyle",atname:"mathvariant",atval:"italic",ttype:UNARY},{input:"\\mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\texttt",tag:"mstyle",atname:"mathvariant",atval:"monospace",ttype:UNARY},{input:"\\mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",ttype:UNARY},{input:"\\mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",ttype:UNARY,codes:LMbbb},{input:"\\mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",ttype:UNARY,codes:LMcal},{input:"\\mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",ttype:UNARY,codes:LMfrk}];function compareNames(g,f){if(g.input>f.input){return 1;}else{return -1;}}var LMnames=[];function LMinitSymbols(){LMsymbols.sort(compareNames);for(i=0;i>1;if(g[f]=LMnames[f];}LMpreviousSymbol=LMcurrentSymbol;if(m!=""){LMcurrentSymbol=LMsymbols[l].ttype;return LMsymbols[l];}LMcurrentSymbol=CONST;f=1;s=q.slice(0,1);if("0"<=s&&s<="9"){r="mn";}else{r=(("A">s||s>"Z")&&("a">s||s>"z")?"mo":"mi");}return{input:s,tag:r,output:s,ttype:CONST};}var LMpreviousSymbol,LMcurrentSymbol;function LMparseSexpr(v){var z,w,q,f,D,s,r=document.createDocumentFragment();v=LMremoveCharsAndBlanks(v,0);z=LMgetSymbol(v);if(z==null||z.ttype==RIGHTBRACKET){return[null,v,null];}if(z.ttype==DEFINITION){v=z.output+LMremoveCharsAndBlanks(v,z.input.length);z=LMgetSymbol(v);if(z==null||z.ttype==RIGHTBRACKET){return[null,v,null];}}v=LMremoveCharsAndBlanks(v,z.input.length);switch(z.ttype){case SPACE:w=LMcreateElementMathML(z.tag);w.setAttribute(z.atname,z.atval);return[w,v,z.tag];case UNDEROVER:if(isIE){if(z.input.substr(0,4)=="\\big"){v="\\"+z.input.substr(4)+v;z=LMgetSymbol(v);z.ttype=UNDEROVER;v=LMremoveCharsAndBlanks(v,z.input.length);}}return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];case CONST:var m=z.output;if(isIE){if(z.input=="'"){m="\u2032";}else{if(z.input=="''"){m="\u2033";}else{if(z.input=="'''"){m="\u2033\u2032";}else{if(z.input=="''''"){m="\u2033\u2033";}else{if(z.input=="\\square"){m="\u25A1";}else{if(z.input.substr(0,5)=="\\frac"){var h=z.input.substr(6,1);if(h=="5"||h=="6"){v=z.input.replace(/\\frac/,"\\frac ")+v;return[w,v,z.tag];}}}}}}}}w=LMcreateMmlNode(z.tag,document.createTextNode(m));return[w,v,z.tag];case LONG:w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));w.setAttribute("minsize","1.5");w.setAttribute("maxsize","1.5");w=LMcreateMmlNode("mover",w);w.appendChild(LMcreateElementMathML("mspace"));return[w,v,z.tag];case STRETCHY:if(isIE&&z.input=="\\backslash"){z.output="\\";}w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));if(z.input=="|"||z.input=="\\vert"||z.input=="\\|"||z.input=="\\Vert"){w.setAttribute("lspace","0em");w.setAttribute("rspace","0em");}w.setAttribute("maxsize",z.atval);if(z.rtag!=null){return[w,v,z.rtag];}else{return[w,v,z.tag];}case BIG:var l=z.atval;if(isIE){l=z.ieval;}z=LMgetSymbol(v);if(z==null){return[null,v,null];}v=LMremoveCharsAndBlanks(v,z.input.length);w=LMcreateMmlNode(z.tag,document.createTextNode(z.output));if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("height",l+"ex");w=LMcreateMmlNode("mrow",w);w.appendChild(F);}else{w.setAttribute("minsize",l);w.setAttribute("maxsize",l);}return[w,v,z.tag];case LEFTBRACKET:if(z.input=="\\left"){z=LMgetSymbol(v);if(z!=null){if(z.input=="."){z.invisible=true;}v=LMremoveCharsAndBlanks(v,z.input.length);}}q=LMparseExpr(v,true,false);if(z==null||(typeof z.invisible=="boolean"&&z.invisible)){w=LMcreateMmlNode("mrow",q[0]);}else{w=LMcreateMmlNode("mo",document.createTextNode(z.output));w=LMcreateMmlNode("mrow",w);w.appendChild(q[0]);}return[w,q[1],q[2]];case MATRIX:if(z.input=="\\begin{array}"){var B="";z=LMgetSymbol(v);v=LMremoveCharsAndBlanks(v,0);if(z==null){B="l";}else{v=LMremoveCharsAndBlanks(v,z.input.length);if(z.input!="{"){B="l";}else{do{z=LMgetSymbol(v);if(z!=null){v=LMremoveCharsAndBlanks(v,z.input.length);if(z.input!="}"){B=B+z.input;}}}while(z!=null&&z.input!=""&&z.input!="}");}}q=LMparseExpr("{"+v,true,true);w=LMcreateMmlNode("mtable",q[0]);B=B.replace(/l/g,"left ");B=B.replace(/r/g,"right ");B=B.replace(/c/g,"center ");w.setAttribute("columnalign",B);w.setAttribute("displaystyle","false");if(isIE){return[w,q[1],null];}var k=LMcreateElementMathML("mspace");k.setAttribute("width","0.167em");var E=LMcreateElementMathML("mspace");E.setAttribute("width","0.167em");var g=LMcreateMmlNode("mrow",k);g.appendChild(w);g.appendChild(E);return[g,q[1],null];}else{q=LMparseExpr("{"+v,true,true);w=LMcreateMmlNode("mtable",q[0]);if(isIE){w.setAttribute("columnspacing","0.25em");}else{w.setAttribute("columnspacing","0.167em");}w.setAttribute("columnalign","right center left");w.setAttribute("displaystyle","true");w=LMcreateMmlNode("mrow",w);return[w,q[1],null];}case TEXT:if(v.charAt(0)=="{"){D=v.indexOf("}");}else{D=0;}if(D==-1){D=v.length;}s=v.slice(1,D);if(s.charAt(0)==" "){w=LMcreateElementMathML("mspace");w.setAttribute("width","0.33em");r.appendChild(w);}r.appendChild(LMcreateMmlNode(z.tag,document.createTextNode(s)));if(s.charAt(s.length-1)==" "){w=LMcreateElementMathML("mspace");w.setAttribute("width","0.33em");r.appendChild(w);}v=LMremoveCharsAndBlanks(v,D+1);return[LMcreateMmlNode("mrow",r),v,null];case UNARY:q=LMparseSexpr(v);if(q[0]==null){return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v];}if(typeof z.func=="boolean"&&z.func){s=v.charAt(0);if(s=="^"||s=="_"||s==","){return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];}else{w=LMcreateMmlNode("mrow",LMcreateMmlNode(z.tag,document.createTextNode(z.output)));if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("width","0.167em");w.appendChild(F);}w.appendChild(q[0]);return[w,q[1],z.tag];}}if(z.input=="\\sqrt"){if(isIE){var F=LMcreateElementMathML("mspace");F.setAttribute("height","1.2ex");F.setAttribute("width","0em");w=LMcreateMmlNode(z.tag,q[0]);w.appendChild(F);return[w,q[1],z.tag];}else{return[LMcreateMmlNode(z.tag,q[0]),q[1],z.tag];}}else{if(typeof z.acc=="boolean"&&z.acc){w=LMcreateMmlNode(z.tag,q[0]);var m=z.output;if(isIE){if(z.input=="\\hat"){m="\u0302";}else{if(z.input=="\\widehat"){m="\u005E";}else{if(z.input=="\\bar"){m="\u00AF";}else{if(z.input=="\\grave"){m="\u0300";}else{if(z.input=="\\tilde"){m="\u0303";}}}}}}var g=LMcreateMmlNode("mo",document.createTextNode(m));if(z.input=="\\vec"||z.input=="\\check"){g.setAttribute("maxsize","1.2");}if(isIE&&z.input=="\\bar"){g.setAttribute("maxsize","0.5");}if(z.input=="\\underbrace"||z.input=="\\underline"){g.setAttribute("accentunder","true");}else{g.setAttribute("accent","true");}w.appendChild(g);if(z.input=="\\overbrace"||z.input=="\\underbrace"){w.ttype=UNDEROVER;}return[w,q[1],z.tag];}else{if(!isIE&&typeof z.codes!="undefined"){for(D=0;D64&&s.charCodeAt(A)<91){o=o+String.fromCharCode(z.codes[s.charCodeAt(A)-65]);}else{o=o+s.charAt(A);}}if(q[0].nodeName=="mi"){q[0]=LMcreateElementMathML("mo").appendChild(document.createTextNode(o));}else{q[0].replaceChild(LMcreateElementMathML("mo").appendChild(document.createTextNode(o)),q[0].childNodes[D]);}}}}w=LMcreateMmlNode(z.tag,q[0]);w.setAttribute(z.atname,z.atval);if(z.input=="\\scriptstyle"||z.input=="\\scriptscriptstyle"){w.setAttribute("displaystyle","false");}return[w,q[1],z.tag];}}case BINARY:q=LMparseSexpr(v);if(q[0]==null){return[LMcreateMmlNode("mo",document.createTextNode(z.input)),v,null];}f=LMparseSexpr(q[1]);if(f[0]==null){return[LMcreateMmlNode("mo",document.createTextNode(z.input)),v,null];}if(z.input=="\\root"||z.input=="\\stackrel"){r.appendChild(f[0]);}r.appendChild(q[0]);if(z.input=="\\frac"){r.appendChild(f[0]);}return[LMcreateMmlNode(z.tag,r),f[1],z.tag];case INFIX:v=LMremoveCharsAndBlanks(v,z.input.length);return[LMcreateMmlNode("mo",document.createTextNode(z.output)),v,z.tag];default:return[LMcreateMmlNode(z.tag,document.createTextNode(z.output)),v,z.tag];}}function LMparseIexpr(l){var k,h,g,j,o,q,m;l=LMremoveCharsAndBlanks(l,0);h=LMgetSymbol(l);o=LMparseSexpr(l);j=o[0];l=o[1];q=o[2];k=LMgetSymbol(l);if(k.ttype==INFIX){l=LMremoveCharsAndBlanks(l,k.input.length);o=LMparseSexpr(l);if(o[0]==null){o[0]=LMcreateMmlNode("mo",document.createTextNode("\u25A1"));}l=o[1];q=o[2];if(k.input=="_"||k.input=="^"){g=LMgetSymbol(l);q=null;m=((h.ttype==UNDEROVER)||(j.ttype==UNDEROVER));if(k.input=="_"&&g.input=="^"){l=LMremoveCharsAndBlanks(l,g.input.length);var f=LMparseSexpr(l);l=f[1];q=f[2];j=LMcreateMmlNode((m?"munderover":"msubsup"),j);j.appendChild(o[0]);j.appendChild(f[0]);}else{if(k.input=="_"){j=LMcreateMmlNode((m?"munder":"msub"),j);j.appendChild(o[0]);}else{j=LMcreateMmlNode((m?"mover":"msup"),j);j.appendChild(o[0]);}}j=LMcreateMmlNode("mrow",j);}else{j=LMcreateMmlNode(k.tag,j);if(k.input=="\\atop"||k.input=="\\choose"){j.setAttribute("linethickness","0ex");}j.appendChild(o[0]);if(k.input=="\\choose"){j=LMcreateMmlNode("mfenced",j);}}}return[j,l,q];}function LMparseExpr(s,r,B){var A,v,l,E,I,o=document.createDocumentFragment();do{s=LMremoveCharsAndBlanks(s,0);l=LMparseIexpr(s);v=l[0];s=l[1];I=l[2];A=LMgetSymbol(s);if(v!=undefined){if((I=="mn"||I=="mi")&&A!=null&&typeof A.func=="boolean"&&A.func){var H=LMcreateElementMathML("mspace");H.setAttribute("width","0.167em");v=LMcreateMmlNode("mrow",v);v.appendChild(H);}o.appendChild(v);}}while((A.ttype!=RIGHTBRACKET)&&A!=null&&A.output!="");I=null;if(A.ttype==RIGHTBRACKET){if(A.input=="\\right"){s=LMremoveCharsAndBlanks(s,A.input.length);A=LMgetSymbol(s);if(A!=null&&A.input=="."){A.invisible=true;}if(A!=null){I=A.rtag;}}if(A!=null){s=LMremoveCharsAndBlanks(s,A.input.length);}var F=o.childNodes.length;if(B&&F>0&&o.childNodes[F-1].nodeName=="mrow"&&F>1&&o.childNodes[F-2].nodeName=="mo"&&o.childNodes[F-2].firstChild.nodeValue=="&"){var g=[];var w=o.childNodes.length;for(E=0;B&&E2){o.removeChild(o.firstChild);o.removeChild(o.firstChild);}G.appendChild(LMcreateMmlNode("mtr",h));}return[G,s];}if(typeof A.invisible!="boolean"||!A.invisible){v=LMcreateMmlNode("mo",document.createTextNode(A.output));o.appendChild(v);}}return[o,s,I];}function LMparseMath(j){var f,h=LMcreateElementMathML("mstyle");if(LMmathcolor!=""){h.setAttribute("mathcolor",LMmathcolor);}if(LMmathfontfamily!=""){h.setAttribute("fontfamily",LMmathfontfamily);}h.appendChild(LMparseExpr(j.replace(/^\s+/g,""),false,false)[0]);h=LMcreateMmlNode("math",h);if(LMshowasciiformulaonhover){h.setAttribute("title",j.replace(/\s+/g," "));}var g=LMcreateElementXHTML("span");g.style.fontSize=mathfontsize;if(LMmathfontfamily!=""){g.style.fontFamily=LMmathfontfamily;}g.appendChild(h);return g;}function LMstrarr2docFrag(f,k){var o=document.createDocumentFragment();var m=false;for(var l=0;l1||q){if(LMcheckForMathML){LMcheckForMathML=false;var h=LMisMathMLavailable();LMnoMathML=h!=null;if(LMnoMathML&&LMnotifyIfNoMathML){if(LMalertIfNoMathML){alert("To view the ASCIIMathML notation use Internet Explorer 6 +\nMathPlayer (free from www.dessci.com)\n or Firefox/Mozilla/Netscape");}else{LMbody.insertBefore(h,LMbody.childNodes[0]);}}}if(!LMnoMathML){f=LMstrarr2docFrag(k,g.nodeType==8);var l=f.childNodes.length;g.parentNode.replaceChild(f,g);return l-1;}else{return 0;}}}}else{return 0;}}else{if(g.nodeName!="math"){for(j=0;j$\\displaystyle{$1}$

');f=f.replace(/\\begin{(theorem|lemma|proposition|corollary)}((.|\n)*?)\\end{\1}/g,function(j,h,g){tcnt++;return""+h.charAt(0).toUpperCase()+h.slice(1)+" "+tcnt+". "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+"";});f=f.replace(/\\begin{(definition|example|remark|problem|exercise|conjecture|solution)}((.|\n)*?)\\end{\1}/g,function(j,h,g){dcnt++;return""+h.charAt(0).toUpperCase()+h.slice(1)+" "+dcnt+". "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"");});f=f.replace(/\\begin{proof}((.|\n)*?)\\end{proof}/g,function(h,g){return"Proof: "+g.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+" □";});f=f.replace(/\\emph{(.*?)}/g,"$1");f=f.replace(/\\textbf{(.*?)}/g,"$1");f=f.replace(/\\cite{(.*?)}/g,"[$1]");f=f.replace(/\\chapter{(.*?)}/g,"

$1

");f=f.replace(/\\section{(.*?)}(\s*<\/?(br|p)\s?\/?>)?/g,"

$1

");f=f.replace(/\\subsection{(.*?)}/g,"

$1

");f=f.replace(/\\begin{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"
    ");f=f.replace(/\\item\s((.|\n)*?)(?=(\\item|\\end))/g,"
  • $1
    • ");f=f.replace(/\\end{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"
");f=f.replace(/\\begin{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"
    ");f=f.replace(/\\end{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"
");f=f.replace(/\\item\[(.*?)]{(.*?)}/g,"
$1
$2
");f=f.replace(/\\begin{description}/g,"
");f=f.replace(/\\end{description}/g,"
");f=f.replace(/\\newline\b/g,"
");f=f.replace(/\\newpage\b/g,'
');f=f.replace(/\\par\b/g,"

 

");f=f.replace(/\\bigskip/g,'

 

');f=f.replace(/\\medskip/g,'

 

');f=f.replace(/\\smallskip/g,'

 

');f=f.replace(/\\begin{center}(.*?)\\end{center}/g,'

$1

');f=f.replace(//gi,"\n")+"'/>";});f=f.replace(/insertASCIIMathCalculator/g,'
');return f;}function LMprocessNode(o,g,k){var m,f;if(k!=null){m=document.getElementsByTagName("span");for(var h=0;h(.*?)<\/sup>(\s|(\S))/gi,"^{$1} $3");f=f.replace(/(Proof:)/g,"$1");f=f.replace(/QED/g,"□");f=f.replace(/(\\?end{?a?math}?)/ig,"$1");f=f.replace(/(\bamath|\\begin{a?math})/ig,"$1");f=f.replace(/([>\n])(Theorem|Lemma|Proposition|Corollary|Definition|Example|Remark|Problem|Exercise|Conjecture|Solution)(:|\W\W?(\w|\.)*?\W?:)/g,"$1$2$3");}f=f.replace(/%7E/g,"~");if(!avoidinnerHTML){o.innerHTML=f;}LMprocessNodeR(o,g);}}if(isIE){m=document.getElementsByTagName("math");for(var h=0;h');document.write('');}var checkIfSVGavailable=true;var notifyIfNoSVG=true;var alertIfNoSVG=false;var defaultwidth=300;defaultheight=200;var defaultxmin=-5.5;defaultxmax=5.5;var defaultborder=0;border=defaultborder;var defaultstrokewidth="1";var defaultstroke="blue";var defaultstrokeopacity=1;var defaultstrokedasharray=null;var defaultfill="none";var defaultfillopacity=1;var defaultfontstyle="normal";var defaultfontfamily="times";var defaultfontsize="16";var defaultfontweight="normal";var defaultfontstroke="none";var defaultfontfill="none";var defaultmarker="none";var defaultendpoints="";var showcoordinates=true;var markerstrokewidth="1";var markerstroke="black";var markerfill="yellow";var markersize=4;var arrowfill=stroke;var dotradius=4;var ticklength=4;var axesstroke="black";var gridstroke="grey";var backgroundstyle="fill-opacity:0; fill:white";var singlelettersitalic=true;var picturepos=null;var xunitlength;var yunitlength;var origin=[0,0];var above="above";var below="below";var left="left";var right="right";var aboveleft="aboveleft";var aboveright="aboveright";var belowleft="belowleft";var belowright="belowright";var xmin,xmax,ymin,ymax,xscl,yscl,xgrid,ygrid,xtick,ytick,initialized;var strokewidth,strokedasharray,stroke,fill,strokeopacity,fillopacity;var fontstyle,fontfamily,fontsize,fontweight,fontstroke,fontfill;var marker,endpoints,dynamic={};var picture,svgpicture,doc,width,height,a,b,c,d,i,n,p,t,x,y;var isIE=document.createElementNS==null;var cpi="\u03C0",ctheta="\u03B8";var log=function(f){return ln(f)/ln(10);};var pi=Math.PI,e=Math.E,ln=Math.log,sqrt=Math.sqrt;var floor=Math.floor,ceil=Math.ceil,abs=Math.abs;var sin=Math.sin,cos=Math.cos,tan=Math.tan;var arcsin=Math.asin,arccos=Math.acos,arctan=Math.atan;var sec=function(f){return 1/Math.cos(f);};var csc=function(f){return 1/Math.sin(f);};var cot=function(f){return 1/Math.tan(f);};var arcsec=function(f){return arccos(1/f);};var arccsc=function(f){return arcsin(1/f);};var arccot=function(f){return arctan(1/f);};var sinh=function(f){return(Math.exp(f)-Math.exp(-f))/2;};var cosh=function(f){return(Math.exp(f)+Math.exp(-f))/2;};var tanh=function(f){return(Math.exp(f)-Math.exp(-f))/(Math.exp(f)+Math.exp(-f));};var sech=function(f){return 1/cosh(f);};var csch=function(f){return 1/sinh(f);};var coth=function(f){return 1/tanh(f);};var arcsinh=function(f){return ln(f+Math.sqrt(f*f+1));};var arccosh=function(f){return ln(f+Math.sqrt(f*f-1));};var arctanh=function(f){return ln((1+f)/(1-f))/2;};var sech=function(f){return 1/cosh(f);};var csch=function(f){return 1/sinh(f);};var coth=function(f){return 1/tanh(f);};var arcsech=function(f){return arccosh(1/f);};var arccsch=function(f){return arcsinh(1/f);};var arccoth=function(f){return arctanh(1/f);};var sign=function(f){return(f==0?0:(f<0?-1:1));};function factorial(f,h){if(h==null){h=1;}if(Math.abs(f-Math.round(f*1000000)/1000000)<1e-15){f=Math.round(f*1000000)/1000000;}if(f-Math.floor(f)!=0){return NaN;}for(var g=f-h;g>0;g-=h){f*=g;}return(f<0?NaN:(f==0?1:f));}function C(f,g){var j=1;for(var h=0;h0){if(alertIfNoSVG){alert("To view the SVG pictures in Internet Explorer\ndownload the free Adobe SVGviewer from www.adobe.com/svg or\nuse Firefox 2.0 or later");}else{g.insertBefore(m,g.childNodes[0]);}}}if(m==null){for(s=0;s=xmax){alert("Picture requires at least two numbers: xmin < xmax");}else{if(f!=null&&(typeof h!="number"||typeof f!="number"||h>=f)){alert("initPicture(xmin,xmax,ymin,ymax) requires numbers ymin < ymax");}else{if(width==null){width=picture.getAttribute("width");if(width==null||width==""){width=defaultwidth;}}picture.setAttribute("width",width);if(height==null){height=picture.getAttribute("height");if(height==null||height==""){height=defaultheight;}}picture.setAttribute("height",height);xunitlength=(width-2*border)/(xmax-xmin);yunitlength=xunitlength;if(ymin==null){origin=[-xmin*xunitlength+border,height/2];ymin=-(height-2*border)/(2*yunitlength);ymax=-ymin;}else{if(ymax!=null){yunitlength=(height-2*border)/(ymax-ymin);}else{ymax=(height-2*border)/yunitlength+ymin;}origin=[-xmin*xunitlength+border,-ymin*yunitlength+border];}if(isIE){if(picture.FULLSCREEN==undefined){setTimeout("drawPictures()",50);throw"wait";}svgpicture=picture.getSVGDocument().getElementById("root");if(svgpicture==null){setTimeout("drawPictures()",50);throw"wait";}svgpicture=picture.getSVGDocument().getElementById("root");while(svgpicture.childNodes.length>0){svgpicture.removeChild(svgpicture.lastChild);}svgpicture.setAttribute("width",width);svgpicture.setAttribute("height",height);svgpicture.setAttribute("name",picture.getAttribute("id"));doc=picture.getSVGDocument();var l=document.getElementById(picture.getAttribute("id")+"mml");if(l!=null){while(l.childNodes.length>0){l.removeChild(l.lastChild);}}}else{var g=document.createElementNS("http://www.w3.org/2000/svg","svg");g.setAttribute("id",picture.getAttribute("id"));g.setAttribute("name",picture.getAttribute("id"));g.setAttribute("style","display:inline");g.setAttribute("width",picture.getAttribute("width"));g.setAttribute("height",picture.getAttribute("height"));picturepos=findPos(picture);g.setAttribute("left",picturepos[0]);g.setAttribute("top",picturepos[1]);if(picture.parentNode!=null){picture.parentNode.replaceChild(g,picture);}else{svgpicture.parentNode.replaceChild(g,svgpicture);}svgpicture=g;doc=document;}svgpicture.setAttribute("xunitlength",xunitlength);svgpicture.setAttribute("yunitlength",yunitlength);svgpicture.setAttribute("xmin",xmin);svgpicture.setAttribute("xmax",xmax);svgpicture.setAttribute("ymin",ymin);svgpicture.setAttribute("ymax",ymax);svgpicture.setAttribute("ox",origin[0]);svgpicture.setAttribute("oy",origin[1]);var j=myCreateElementSVG("rect");j.setAttribute("x","0");j.setAttribute("y","0");j.setAttribute("width",width);j.setAttribute("height",height);j.setAttribute("style",backgroundstyle);svgpicture.appendChild(j);svgpicture.setAttribute("onmousemove","displayCoord(evt)");svgpicture.setAttribute("onmouseout","removeCoord(evt)");svgpicture.setAttribute("onclick","mClick(evt)");j=myCreateElementSVG("text");j.appendChild(doc.createTextNode(" "));svgpicture.appendChild(j);border=defaultborder;}}}}function line(j,h,k,g){var f;if(k!=null){f=doc.getElementById(k);}if(f==null){f=myCreateElementSVG("path");f.setAttribute("id",k);svgpicture.appendChild(f);}f.setAttribute("d","M"+(j[0]*xunitlength+origin[0])+","+(height-j[1]*yunitlength-origin[1])+" "+(h[0]*xunitlength+origin[0])+","+(height-h[1]*yunitlength-origin[1]));f.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null){f.setAttribute("stroke-dasharray",strokedasharray);}f.setAttribute("stroke",stroke);f.setAttribute("fill",fill);f.setAttribute("stroke-opacity",strokeopacity);f.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot"){ASdot(j,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(j,h);}ASdot(h,markersize,markerstroke,markerfill);}else{if(marker=="arrow"){arrowhead(j,h);}}if(g==null&&endpoints!=""){g=endpoints;}if(g!=null){if(g.indexOf("<-")!=-1){arrowhead(h,j);}if(g.indexOf("o-")!=-1){dot(j,"open");}if(g.indexOf("*-")!=-1){dot(j,"closed");}if(g.indexOf("->")!=-1){arrowhead(j,h);}if(g.indexOf("-o")!=-1){dot(h,"open");}if(g.indexOf("-*")!=-1){dot(h,"closed");}}}function path(k,m,l,j){if(l==null){l="";}var h,f,g;if(m!=null){h=doc.getElementById(m);}if(h==null){h=myCreateElementSVG("path");h.setAttribute("id",m);svgpicture.appendChild(h);}if(typeof k=="string"){f=k;}else{f="M";f+=(k[0][0]*xunitlength+origin[0])+","+(height-k[0][1]*yunitlength-origin[1])+" "+l;for(g=1;g")!=-1){arrowhead(k[k.length-2],k[k.length-1]);}if(j.indexOf("-o")!=-1){dot(k[k.length-1],"open");}if(j.indexOf("-*")!=-1){dot(k[k.length-1],"closed");}}}function curve(g,h,f){path(g,h,"T",f);}function vector(g,f,h){line(g,f,h,"","->");}function circle(g,f,j){var h;if(j!=null){h=doc.getElementById(j);}if(h==null){h=myCreateElementSVG("circle");h.setAttribute("id",j);svgpicture.appendChild(h);}h.setAttribute("cx",g[0]*xunitlength+origin[0]);h.setAttribute("cy",height-g[1]*yunitlength-origin[1]);h.setAttribute("r",f*xunitlength);h.setAttribute("stroke-width",strokewidth);h.setAttribute("stroke",stroke);h.setAttribute("fill",fill);h.setAttribute("stroke-opacity",strokeopacity);h.setAttribute("fill-opacity",fillopacity);}function loop(f,g,h){if(g==null){g=[1,0];}path([f,[f[0]+g[0],f[1]+g[1]],[f[0]-g[1],f[1]+g[0]],f],h,"C");if(marker=="arrow"||marker=="arrowdot"){arrowhead([f[0]+Math.cos(1.4)*g[0]-Math.sin(1.4)*g[1],f[1]+Math.sin(1.4)*g[0]+Math.cos(1.4)*g[1]],f);}}function arc(l,g,f,k){var j,h;if(k!=null){j=doc.getElementById(k);}if(f==null){h=[g[0]-l[0],g[1]-l[1]];f=Math.sqrt(h[0]*h[0]+h[1]*h[1]);}if(j==null){j=myCreateElementSVG("path");j.setAttribute("id",k);svgpicture.appendChild(j);}j.setAttribute("d","M"+(l[0]*xunitlength+origin[0])+","+(height-l[1]*yunitlength-origin[1])+" A"+f*xunitlength+","+f*yunitlength+" 0 0,0 "+(g[0]*xunitlength+origin[0])+","+(height-g[1]*yunitlength-origin[1]));j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);j.setAttribute("fill",fill);j.setAttribute("stroke-opacity",strokeopacity);j.setAttribute("fill-opacity",fillopacity);if(marker=="arrow"||marker=="arrowdot"){u=[(g[1]-l[1])/4,(l[0]-g[0])/4];h=[(g[0]-l[0])/2,(g[1]-l[1])/2];h=[l[0]+h[0]+u[0],l[1]+h[1]+u[1]];}else{h=[l[0],l[1]];}if(marker=="dot"||marker=="arrowdot"){ASdot(l,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(h,g);}ASdot(g,markersize,markerstroke,markerfill);}else{if(marker=="arrow"){arrowhead(h,g);}}}function sector(f,l,g,k){var j=l[0]-f[0],h=l[1]-f[1];arc(l,g,Math.sqrt(j*j+h*h),k+"arc");path([g,f,l],k+"path");}function ellipse(f,j,h,k){var g;if(k!=null){g=doc.getElementById(k);}if(g==null){g=myCreateElementSVG("ellipse");g.setAttribute("id",k);svgpicture.appendChild(g);}g.setAttribute("cx",f[0]*xunitlength+origin[0]);g.setAttribute("cy",height-f[1]*yunitlength-origin[1]);g.setAttribute("rx",j*xunitlength);g.setAttribute("ry",h*yunitlength);g.setAttribute("stroke-width",strokewidth);g.setAttribute("stroke",stroke);g.setAttribute("fill",fill);g.setAttribute("stroke-opacity",strokeopacity);g.setAttribute("fill-opacity",fillopacity);}function triangle(h,g,f,j){path([h,g,f,h],j);}function rect(k,h,l,j,g){var f;if(l!=null){f=doc.getElementById(l);}if(f==null){f=myCreateElementSVG("rect");f.setAttribute("id",l);svgpicture.appendChild(f);}f.setAttribute("x",k[0]*xunitlength+origin[0]);f.setAttribute("y",height-h[1]*yunitlength-origin[1]);f.setAttribute("width",(h[0]-k[0])*xunitlength);f.setAttribute("height",(h[1]-k[1])*yunitlength);if(j!=null){f.setAttribute("rx",j*xunitlength);}if(g!=null){f.setAttribute("ry",g*yunitlength);}f.setAttribute("stroke-width",strokewidth);f.setAttribute("stroke",stroke);f.setAttribute("fill",fill);f.setAttribute("stroke-opacity",strokeopacity);f.setAttribute("fill-opacity",fillopacity);}function text(g,q,l,f,m){var k,j,r=0,o=fontsize/3;if(/(`|\$)/.test(q)){k=document.getElementById(svgpicture.getAttribute("name")+"mml");if(k!=null){if(f!=null){j=document.getElementById(f);}if(j==null){j=myCreateElementXHTML("div");j.setAttribute("id",f);j.style.position="absolute";k.appendChild(j);}while(j.childNodes.length>0){j.removeChild(j.lastChild);}j.appendChild(document.createTextNode(q));j.style.left=""+(g[0]*xunitlength+origin[0])+"px";j.style.top=""+(height-g[1]*yunitlength-origin[1])+"px";if(/`/.test(q)){AMprocessNode(j);}else{LMprocessNode(j);}r=-j.offsetWidth/2;o=-j.offsetHeight/2;if(l!=null){if(/above/.test(l)){o=-j.offsetHeight;}if(/below/.test(l)){o=0;}if(/right/.test(l)){r=0;}if(/left/.test(l)){r=-j.offsetWidth;}}j.style.left=""+(g[0]*xunitlength+origin[0]+r)+"px";j.style.top=""+(height-g[1]*yunitlength-origin[1]+o)+"px";}return g;}var h="middle";if(l!=null){if(/above/.test(l)){o=-fontsize/2;}if(/below/.test(l)){o=fontsize-0;}if(/right/.test(l)){h="start";r=fontsize/4;}if(/left/.test(l)){h="end";r=-fontsize/4;}}if(f!=null){j=doc.getElementById(f);}if(j==null){j=myCreateElementSVG("text");j.setAttribute("id",f);svgpicture.appendChild(j);j.appendChild(doc.createTextNode(q));}while(j.childNodes.length>1){j.removeChild(j.lastChild);}j.lastChild.nodeValue="\xA0"+q+"\xA0";j.setAttribute("x",g[0]*xunitlength+origin[0]+r);j.setAttribute("y",height-g[1]*yunitlength-origin[1]+o);j.setAttribute("font-style",(m!=null?m:(q.search(/^[a-zA-Z]$/)!=-1?"italic":fontstyle)));j.setAttribute("font-family",fontfamily);j.setAttribute("font-size",fontsize);j.setAttribute("font-weight",fontweight);j.setAttribute("text-anchor",h);if(fontstroke!="none"){j.setAttribute("stroke",fontstroke);}if(fontfill!="none"){j.setAttribute("fill",fontfill);}return g;}function mtext(l,h,o,m){var j="middle";var g=0;var f=fontsize/3;if(o!=null){if(o.slice(0,5)=="above"){f=-fontsize/2;}if(o.slice(0,5)=="below"){f=fontsize-0;}if(o.slice(0,5)=="right"||o.slice(5,10)=="right"){j="start";g=fontsize/2;}if(o.slice(0,4)=="left"||o.slice(5,9)=="left"){j="end";g=-fontsize/2;}}var k=this;if(this.nodeName=="svg"){k=myCreateElementSVG("text");this.appendChild(k);k.appendChild(doc.createTextNode(h));}k.lastChild.nodeValue=h;k.setAttribute("x",l[0]+g);k.setAttribute("y",l[1]+f);k.setAttribute("font-style",(m!=null?m:fontstyle));k.setAttribute("font-family",fontfamily);k.setAttribute("font-size",fontsize);k.setAttribute("font-weight",fontweight);k.setAttribute("text-anchor",j);if(fontstroke!="none"){k.setAttribute("stroke",fontstroke);}if(fontfill!="none"){k.setAttribute("fill",fontfill);}}function image(g,l,f,j,m){var k;if(m!=null){k=doc.getElementById(m);}if(k==null){k=myCreateElementSVG("image");k.setAttribute("id",m);svgpicture.appendChild(k);}k.setAttribute("x",l[0]*xunitlength+origin[0]);k.setAttribute("y",height-l[1]*yunitlength-origin[1]);k.setAttribute("width",f);k.setAttribute("height",j);k.setAttribute("xlink:href",g);}function ASdot(h,g,j,l){if(j==null){j=stroke;}if(l==null){l=fill;}var k=myCreateElementSVG("circle");k.setAttribute("cx",h[0]*xunitlength+origin[0]);k.setAttribute("cy",height-h[1]*yunitlength-origin[1]);k.setAttribute("r",g);k.setAttribute("stroke-width",strokewidth);k.setAttribute("stroke",j);k.setAttribute("fill",l);svgpicture.appendChild(k);}function dot(g,k,h,o,m){var j;var f=g[0]*xunitlength+origin[0];var l=height-g[1]*yunitlength-origin[1];if(m!=null){j=doc.getElementById(m);}if(k=="+"||k=="-"||k=="|"){if(j==null){j=myCreateElementSVG("path");j.setAttribute("id",m);svgpicture.appendChild(j);}if(k=="+"){j.setAttribute("d"," M "+(f-ticklength)+" "+l+" L "+(f+ticklength)+" "+l+" M "+f+" "+(l-ticklength)+" L "+f+" "+(l+ticklength));j.setAttribute("stroke-width",0.5);j.setAttribute("stroke",axesstroke);}else{if(k=="-"){j.setAttribute("d"," M "+(f-ticklength)+" "+l+" L "+(f+ticklength)+" "+l);}else{j.setAttribute("d"," M "+f+" "+(l-ticklength)+" L "+f+" "+(l+ticklength));}j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);}}else{if(j==null){j=myCreateElementSVG("circle");j.setAttribute("id",m);svgpicture.appendChild(j);}j.setAttribute("cx",f);j.setAttribute("cy",l);j.setAttribute("r",dotradius);j.setAttribute("stroke-width",strokewidth);j.setAttribute("stroke",stroke);j.setAttribute("fill",(k=="open"?"white":(k=="closed"?stroke:markerfill)));}if(h!=null){text(g,h,(o==null?"below":o),(m==null?m:m+"label"));}}point=dot;function arrowhead(m,l){var f;var h=[m[0]*xunitlength+origin[0],height-m[1]*yunitlength-origin[1]];var g=[l[0]*xunitlength+origin[0],height-l[1]*yunitlength-origin[1]];var j=[g[0]-h[0],g[1]-h[1]];var o=Math.sqrt(j[0]*j[0]+j[1]*j[1]);if(o>1e-8){j=[j[0]/o,j[1]/o];f=[-j[1],j[0]];var k=myCreateElementSVG("path");k.setAttribute("d","M "+(g[0]-15*j[0]-4*f[0])+" "+(g[1]-15*j[1]-4*f[1])+" L "+(g[0]-3*j[0])+" "+(g[1]-3*j[1])+" L "+(g[0]-15*j[0]+4*f[0])+" "+(g[1]-15*j[1]+4*f[1])+" z");k.setAttribute("stroke-width",markerstrokewidth);k.setAttribute("stroke",stroke);k.setAttribute("fill",stroke);k.setAttribute("stroke-opacity",strokeopacity);k.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(k);}}function chopZ(g){var f=g.indexOf(".");if(f==-1){return g;}for(var h=g.length-1;h>f&&g.charAt(h)=="0";h--){}if(h==f){h--;}return g.slice(0,h+1);}function grid(g,f){axes(g,f,null,g,f);}function noaxes(){if(!initialized){initPicture();}}function axes(dx,dy,labels,gdx,gdy){var x,y,ldx,ldy,lx,ly,lxp,lyp,pnode,st;if(!initialized){initPicture();}if(typeof dx=="string"){labels=dx;dx=null;}if(typeof dy=="string"){gdx=dy;dy=null;}if(xscl!=null){dx=xscl;gdx=xscl;labels=dx;}if(yscl!=null){dy=yscl;gdy=yscl;}if(xtick!=null){dx=xtick;}if(ytick!=null){dy=ytick;}dx=(dx==null?xunitlength:dx*xunitlength);dy=(dy==null?dx:dy*yunitlength);fontsize=Math.min(dx/2,dy/2,16);ticklength=fontsize/4;if(xgrid!=null){gdx=xgrid;}if(ygrid!=null){gdy=ygrid;}if(gdx!=null){gdx=(typeof gdx=="string"?dx:gdx*xunitlength);gdy=(gdy==null?dy:gdy*yunitlength);pnode=myCreateElementSVG("path");st="";for(x=origin[0];x0;x=x-gdx){st+=" M"+x+",0 "+x+","+height;}for(y=height-origin[1];y0;y=y-gdy){st+=" M0,"+y+" "+width+","+y;}pnode.setAttribute("d",st);pnode.setAttribute("stroke-width",0.5);pnode.setAttribute("stroke",gridstroke);pnode.setAttribute("fill",fill);svgpicture.appendChild(pnode);}pnode=myCreateElementSVG("path");st="M0,"+(height-origin[1])+" "+width+","+(height-origin[1])+" M"+origin[0]+",0 "+origin[0]+","+height;for(x=origin[0]+dx;x0;x=x-dx){st+=" M"+x+","+(height-origin[1]+ticklength)+" "+x+","+(height-origin[1]-ticklength);}for(y=height-origin[1]+dy;y0;y=y-dy){st+=" M"+(origin[0]+ticklength)+","+y+" "+(origin[0]-ticklength)+","+y;}if(labels!=null){with(Math){ldx=dx/xunitlength;ldy=dy/yunitlength;lx=(xmin>0||xmax<0?xmin:0);ly=(ymin>0||ymax<0?ymin:0);lxp=(ly==0?"below":"above");lyp=(lx==0?"left":"right");var ddx=floor(1.1-log(ldx)/log(10))+1;var ddy=floor(1.1-log(ldy)/log(10))+1;for(x=ldx;x<=xmax;x=x+ldx){text([x,ly],chopZ(x.toFixed(ddx)),lxp);}for(x=-ldx;xmin<=x;x=x-ldx){text([x,ly],chopZ(x.toFixed(ddx)),lxp);}for(y=ldy;y<=ymax;y=y+ldy){text([lx,y],chopZ(y.toFixed(ddy)),lyp);}for(y=-ldy;ymin<=y;y=y-ldy){text([lx,y],chopZ(y.toFixed(ddy)),lyp);}}}fontsize=defaultfontsize;pnode.setAttribute("d",st);pnode.setAttribute("stroke-width",0.5);pnode.setAttribute("stroke",axesstroke);pnode.setAttribute("fill",fill);pnode.setAttribute("stroke-opacity",strokeopacity);pnode.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(pnode);}function mathjs(h){h=h.replace(/\s/g,"");if(h.indexOf("^-1")!=-1){h=h.replace(/sin\^-1/g,"arcsin");h=h.replace(/cos\^-1/g,"arccos");h=h.replace(/tan\^-1/g,"arctan");h=h.replace(/sec\^-1/g,"arcsec");h=h.replace(/csc\^-1/g,"arccsc");h=h.replace(/cot\^-1/g,"arccot");h=h.replace(/sinh\^-1/g,"arcsinh");h=h.replace(/cosh\^-1/g,"arccosh");h=h.replace(/tanh\^-1/g,"arctanh");h=h.replace(/sech\^-1/g,"arcsech");h=h.replace(/csch\^-1/g,"arccsch");h=h.replace(/coth\^-1/g,"arccoth");}h=h.replace(/^e$/g,"(Math.E)");h=h.replace(/^e([^a-zA-Z])/g,"(Math.E)$1");h=h.replace(/([^a-zA-Z])e/g,"$1(Math.E)");h=h.replace(/([0-9])([\(a-zA-Z])/g,"$1*$2");h=h.replace(/\)([\(0-9a-zA-Z])/g,")*$1");var l,g,f,m,o;while((l=h.indexOf("^"))!=-1){if(l==0){return"Error: missing argument";}g=l-1;m=h.charAt(g);if(m>="0"&&m<="9"){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}if(m=="."){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}}}else{if(m==")"){o=1;g--;while(g>=0&&o>0){m=h.charAt(g);if(m=="("){o--;}else{if(m==")"){o++;}}g--;}while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){g--;while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{return"Error: incorrect syntax in "+h+" at position "+g;}}}if(l==h.length-1){return"Error: missing argument";}f=l+1;m=h.charAt(f);if(m>="0"&&m<="9"||m=="-"){f++;while(f="0"&&m<="9"){f++;}if(m=="."){f++;while(f="0"&&m<="9"){f++;}}}else{if(m=="("){o=1;f++;while(f0){m=h.charAt(f);if(m=="("){o++;}else{if(m==")"){o--;}}f++;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){f++;while(f="a"&&m<="z"||m>="A"&&m<="Z"){f++;}}else{return"Error: incorrect syntax in "+h+" at position "+f;}}}h=h.slice(0,g+1)+"Math.pow("+h.slice(g+1,l)+","+h.slice(l+1,f)+")"+h.slice(f);}while((l=h.indexOf("!"))!=-1){if(l==0){return"Error: missing argument";}g=l-1;m=h.charAt(g);if(m>="0"&&m<="9"){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}if(m=="."){g--;while(g>=0&&(m=h.charAt(g))>="0"&&m<="9"){g--;}}}else{if(m==")"){o=1;g--;while(g>=0&&o>0){m=h.charAt(g);if(m=="("){o--;}else{if(m==")"){o++;}}g--;}while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{if(m>="a"&&m<="z"||m>="A"&&m<="Z"){g--;while(g>=0&&(m=h.charAt(g))>="a"&&m<="z"||m>="A"&&m<="Z"){g--;}}else{return"Error: incorrect syntax in "+h+" at position "+g;}}}h=h.slice(0,g+1)+"factorial("+h.slice(g+1,l)+")"+h.slice(l+1);}return h;}function plot(fun,x_min,x_max,points,id,endpts){var pth=[];var f=function(x){return x;},g=fun;var name=null;if(typeof fun=="string"){eval("g = function(x){ with(Math) return "+mathjs(fun)+" }");}else{if(typeof fun=="object"){eval("f = function(t){ with(Math) return "+mathjs(fun[0])+" }");eval("g = function(t){ with(Math) return "+mathjs(fun[1])+" }");}}if(typeof x_min=="string"){name=x_min;x_min=xmin;}else{name=id;}var min=(x_min==null?xmin:x_min);var max=(x_max==null?xmax:x_max);var inc=max-min-0.000001*(max-min);inc=(points==null?inc/200:inc/points);var gt;for(var t=min;t<=max;t+=inc){gt=g(t);if(!(isNaN(gt)||Math.abs(gt)=="Infinity")){pth[pth.length]=[f(t),gt];}}path(pth,name,null,endpts);return p;}function slopefield(fun,dx,dy){var g=fun;if(typeof fun=="string"){eval("g = function(x,y){ with(Math) return "+mathjs(fun)+" }");}var gxy,x,y,u,v,dz;if(dx==null){dx=1;}if(dy==null){dy=1;}dz=Math.sqrt(dx*dx+dy*dy)/6;var x_min=Math.ceil(xmin/dx);var y_min=Math.ceil(ymin/dy);for(x=x_min;x<=xmax;x+=dx){for(y=y_min;y<=ymax;y+=dy){gxy=g(x,y);if(!isNaN(gxy)){if(Math.abs(gxy)=="Infinity"){u=0;v=dz;}else{u=dz/Math.sqrt(1+gxy*gxy);v=gxy*u;}line([x-u,y-v],[x+u,y+v]);}}}}function show_props(h){var f="";for(var g=0;g\nResult:     \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n
';function generic(){if(translateOnLoad){var g=document.getElementById("processasciimathinmoodle");if(g!=null){dsvglocation=g.className;}if(g!=null||!checkforprocessasciimathinmoodle){if(translateLaTeX){LMtranslate();}if(translateASCIIMath){translate();}if(translateASCIIsvg){drawPictures();}}var f=getElementsByClass(document,"div","ASCIIMathCalculator");if(f.length>0){initASCIIMathCalculators(f);}}}if(typeof window.addEventListener!="undefined"){window.addEventListener("load",generic,false);}else{if(typeof document.addEventListener!="undefined"){document.addEventListener("load",generic,false);}else{if(typeof window.attachEvent!="undefined"){window.attachEvent("onload",generic);}else{if(typeof window.onload=="function"){var existing=onload;window.onload=function(){existing();generic();};}else{window.onload=generic;}}}} \ No newline at end of file