var isIE=(document.createElementNS==null);var checkForMathML=true;var notifyIfNoMathML=true;var alertIfNoMathML=false;var mathcolor="blue";var mathfontfamily="Times New Roman";var displaystyle=true;var showasciiformulaonhover=true;var decimalsign=".";var AMdelimiter1="`",AMescape1="\\\\`";var AMusedelimiter2=true;var AMdelimiter2="$",AMescape2="\\\\\\$",AMdelimiter2regexp="\\$";var doubleblankmathdelimiter=false;//-->
if("undefined"==typeof(AMTcgiloc)){var AMTcgiloc = "http://www.codecogs.com/gif.latex";}
if(document.getElementById==null)
alert("This webpage requires a recent browser such as\nMozilla/Netscape 7+ or Internet Explorer 6+MathPlayer")
function AMcreateElementXHTML(t){if(isIE)return document.createElement(t);else return document.createElementNS("http://www.w3.org/1999/xhtml",t);}function AMnoMathMLNote(){var nd=AMcreateElementXHTML("h3");nd.setAttribute("align","center")
nd.appendChild(AMcreateElementXHTML("p"));nd.appendChild(document.createTextNode("正常显示数学公式需安装 Internet Explorer 6+"));an=AMcreateElementXHTML("a");an.appendChild(document.createTextNode("MathPlayer"));an.setAttribute("href","http://www.dessci.com/en/dl/MathPlayerSetup.asp");nd.appendChild(an);nd.appendChild(document.createTextNode("或 Netscape/Mozilla/Firefox"));nd.appendChild(AMcreateElementXHTML("p"));return nd;}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 ActiveX=new ActiveXObject("MathPlayer.Factory.1");return null;}catch(e){return AMnoMathMLNote();}else return AMnoMathMLNote();}var AMcal=[0xEF35,0x212C,0xEF36,0xEF37,0x2130,0x2131,0xEF38,0x210B,0x2110,0xEF39,0xEF3A,0x2112,0x2133,0xEF3B,0xEF3C,0xEF3D,0xEF3E,0x211B,0xEF3F,0xEF40,0xEF41,0xEF42,0xEF43,0xEF44,0xEF45,0xEF46];var AMfrk=[0xEF5D,0xEF5E,0x212D,0xEF5F,0xEF60,0xEF61,0xEF62,0x210C,0x2111,0xEF63,0xEF64,0xEF65,0xEF66,0xEF67,0xEF68,0xEF69,0xEF6A,0x211C,0xEF6B,0xEF6C,0xEF6D,0xEF6E,0xEF6F,0xEF70,0xEF71,0x2128];var AMbbb=[0xEF8C,0xEF8D,0x2102,0xEF8E,0xEF8F,0xEF90,0xEF91,0x210D,0xEF92,0xEF93,0xEF94,0xEF95,0xEF96,0x2115,0xEF97,0x2119,0x211A,0x211D,0xEF98,0xEF99,0xEF9A,0xEF9B,0xEF9C,0xEF9D,0xEF9E,0x2124];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:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:CONST},
{input:"varsigma",tag:"mi",output:"\u03C2",tex:null,ttype:CONST},
{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:CONST},
{input:"varphi",tag:"mi",output:"\u03D5",tex:null,ttype:CONST},
{input:"varpi",tag:"mi",output:"\u03D6",tex:null,ttype:CONST},
{input:"varrho",tag:"mi",output:"\u03F1",tex:null,ttype:CONST},
{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:CONST},
{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:CONST},
{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:CONST},
{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:CONST},
{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:CONST},
{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:CONST},
{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:CONST},
{input:"theta",tag:"mi",output:"\u03B8",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:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:CONST},
{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:CONST},
{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:CONST},
{input:"omicron",tag:"mi",output:"\u03BF",tex:null,ttype:CONST},
{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:CONST},
{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:CONST},
{input:"sigmaf",tag:"mi",output:"\u03C2",tex:null,ttype:CONST},
{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:CONST},
{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:CONST},
{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:CONST},
{input:"phi",tag:"mi",output:"\u03C6",tex:null,ttype:CONST},
{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:CONST},
{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:CONST},
{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:CONST},
{input:"Alpha",tag:"mo",output:"\u0391",tex:null,ttype:CONST},
{input:"Beta",tag:"mo",output:"\u0392",tex:null,ttype:CONST},
{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:CONST},
{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:CONST},
{input:"Epsilon",tag:"mo",output:"\u0395",tex:null,ttype:CONST},
{input:"Zeta",tag:"mo",output:"\u0396",tex:null,ttype:CONST},
{input:"Eta",tag:"mo",output:"\u0397",tex:null,ttype:CONST},
{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:CONST},
{input:"Iota",tag:"mo",output:"\u0399",tex:null,ttype:CONST},
{input:"Kappa",tag:"mo",output:"\u039A",tex:null,ttype:CONST},
{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:CONST},
{input:"Mu",tag:"mo",output:"\u039C",tex:null,ttype:CONST},
{input:"Nu",tag:"mo",output:"\u039D",tex:null,ttype:CONST},
{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:CONST},
{input:"Omicron",tag:"mo",output:"\u039F",tex:null,ttype:CONST},
{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:CONST},
{input:"Rho",tag:"mo",output:"\u03A1",tex:null,ttype:CONST},
{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:CONST},
{input:"Tau",tag:"mo",output:"\u03A4",tex:null,ttype:CONST},
{input:"Upsilon",tag:"mo",output:"\u03A5",tex:null,ttype:CONST},
{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:CONST},
{input:"Chi",tag:"mo",output:"\u03A7",tex:null,ttype:CONST},
{input:"Psi",tag:"mo",output:"\u03A8",tex:null,ttype:CONST},
{input:"Omega",tag:"mo",output:"\u03A9",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:"div",ttype:CONST},
{input:"divide",tag:"mo",output:"-:",tex:null,ttype:DEFINITION},
{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:"\u2224",tex:"nmid",ttype:CONST},
{input:"!-=",tag:"mo",output:"\u2262",tex:"nequiv",ttype:CONST},
{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:"gt",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:"gt=",tag:"mo",output:"\u2265",tex:"geq",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:"stackrel{\\sim}{=}",ttype:CONST},
{input:"cong",tag:"mo",output:"~=",tex:null,ttype:DEFINITION},
{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:"Rightarrow",ttype:CONST},
{input:"implies",tag:"mo",output:"=>",tex:null,ttype:DEFINITION},
{input:"if",tag:"mo",output:"if",tex:null,ttype:SPACE},
{input:"<=>",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:CONST},
{input:"iff",tag:"mo",output:"<=>",tex:null,ttype:DEFINITION},
{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:"lbrace",ttype:LEFTBRACKET},
{input:"}",tag:"mo",output:"}",tex:"rbrace",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:"-+",tag:"mo",output:"\u2213",tex:"mp",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:"\u2235",tex:"because",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,val:true},
{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:"boxempty",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:"lceil",ttype:CONST},
{input:"lceiling",tag:"mo",output:"|~",tex:null,ttype:DEFINITION},
{input:"~|",tag:"mo",output:"\u2309",tex:"rceil",ttype:CONST},
{input:"rceiling",tag:"mo",output:"~|",tex:null,ttype:DEFINITION},
{input:"CC",tag:"mo",output:"\u2102",tex:"mathbb{C}",ttype:CONST,notexcopy:true},
{input:"NN",tag:"mo",output:"\u2115",tex:"mathbb{N}",ttype:CONST,notexcopy:true},
{input:"QQ",tag:"mo",output:"\u211A",tex:"mathbb{Q}",ttype:CONST,notexcopy:true},
{input:"RR",tag:"mo",output:"\u211D",tex:"mathbb{R}",ttype:CONST,notexcopy:true},
{input:"ZZ",tag:"mo",output:"\u2124",tex:"mathbb{Z}",ttype:CONST,notexcopy:true},
{input:"f",tag:"mi",output:"f",tex:null,ttype:UNARY,func:true,val:true},
{input:"g",tag:"mi",output:"g",tex:null,ttype:UNARY,func:true,val: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:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:UNARY,func:true},
{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:UNARY,func:true},
{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:UNARY,func:true},
{input:"arccot",tag:"mo",output:"arccot",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:"abs",tag:"mo",output:"abs",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:"text{mod}",ttype:CONST},
{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:UNARY,func:true},
{input:"lcm",tag:"mo",output:"lcm",tex:"text{lcm}",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:"mathbf",ttype:UNARY,notexcopy:true},
{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:"mathsf",ttype:UNARY,notexcopy:true},
{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:"mathbb",ttype:UNARY,codes:AMbbb,notexcopy:true},
{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:"mathcal",ttype:UNARY,codes:AMcal,notexcopy:true},
{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:"mathtt",ttype:UNARY,notexcopy:true},
{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:"mathfrak",ttype:UNARY,codes:AMfrk,notexcopy:true},
{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:UNARY,codes:AMfrk}];function compareNames(s1,s2){if(s1.input>s2.input)return 1
else return-1;}var AMnames=[];function AMinitSymbols(){var texsymbols=[],i;for(i=0;i<AMsymbols.length;i++)
if(AMsymbols[i].tex&&!(typeof AMsymbols[i].notexcopy=="boolean"&&AMsymbols[i].notexcopy))
texsymbols[texsymbols.length]={input:AMsymbols[i].tex,
tag:AMsymbols[i].tag,output:AMsymbols[i].output,ttype:AMsymbols[i].ttype};AMsymbols=AMsymbols.concat(texsymbols);AMsymbols.sort(compareNames);for(i=0;i<AMsymbols.length;i++)AMnames[i]=AMsymbols[i].input;}var AMmathml="http://www.w3.org/1998/Math/MathML";function AMcreateElementMathML(t){if(isIE)return document.createElement("m:"+t);else return document.createElementNS(AMmathml,t);}function AMcreateMmlNode(t,frag){if(isIE)var node=document.createElement("m:"+t);else var node=document.createElementNS(AMmathml,t);node.appendChild(frag);return node;}function newcommand(oldstr,newstr){AMsymbols=AMsymbols.concat([{input:oldstr,tag:"mo",output:newstr,
tex:null,ttype:DEFINITION}]);}function AMremoveCharsAndBlanks(str,n){var st;if(str.charAt(n)=="\\"&&str.charAt(n+1)!="\\"&&str.charAt(n+1)!=" ")
st=str.slice(n+1);else st=str.slice(n);for(var i=0;i<st.length&&st.charCodeAt(i)<=32;i=i+1);return st.slice(i);}function AMposition(arr,str,n){if(n==0){var h,m;n=-1;h=arr.length;while(n+1<h){m=(n+h)>>1;if(arr[m]<str)n=m;else h=m;}return h;}else
for(var i=n;i<arr.length&&arr[i]<str;i++);return i;}function AMgetSymbol(str){var k=0;var j=0;var mk;var st;var tagst;var match="";var more=true;for(var i=1;i<=str.length&&more;i++){st=str.slice(0,i);j=k;k=AMposition(AMnames,st,j);if(k<AMnames.length&&str.slice(0,AMnames[k].length)==AMnames[k]){match=AMnames[k];mk=k;i=match.length;}more=k<AMnames.length&&str.slice(0,AMnames[k].length)>=AMnames[k];}AMpreviousSymbol=AMcurrentSymbol;if(match!=""){AMcurrentSymbol=AMsymbols[mk].ttype;return AMsymbols[mk];}AMcurrentSymbol=CONST;k=1;st=str.slice(0,1);var integ=true;while("0"<=st&&st<="9"&&k<=str.length){st=str.slice(k,k+1);k++;}if(st==decimalsign){st=str.slice(k,k+1);if("0"<=st&&st<="9"){integ=false;k++;while("0"<=st&&st<="9"&&k<=str.length){st=str.slice(k,k+1);k++;}}}if((integ&&k>1)||k>2){st=str.slice(0,k-1);tagst="mn";}else{k=2;st=str.slice(0,1);tagst=(("A">st||st>"Z")&&("a">st||st>"z")?"mo":"mi");}if(st=="-"&&AMpreviousSymbol==INFIX){AMcurrentSymbol=INFIX;return{input:st,tag:tagst,output:st,ttype:UNARY,func:true,val:true};}return{input:st,tag:tagst,output:st,ttype:CONST,val:true};}function AMTremoveBrackets(node){var st;if(node.charAt(0)=='{'&&node.charAt(node.length-1)=='}'){st=node.charAt(1);if(st=="("||st=="[")node='{'+node.substr(2);st=node.substr(1,6);if(st=="\\left("||st=="\\left["||st=="\\left{")node='{'+node.substr(7);st=node.substr(1,12);if(st=="\\left\\lbrace"||st=="\\left\\langle")node='{'+node.substr(13);st=node.charAt(node.length-2);if(st==")"||st=="]")node=node.substr(0,node.length-8)+'}';st=node.substr(node.length-8,7)
if(st=="\\rbrace"||st=="\\rangle")node=node.substr(0,node.length-14)+'}';}return node;}function AMremoveBrackets(node){var st;if(node.nodeName=="mrow"){st=node.firstChild.firstChild.nodeValue;if(st=="("||st=="["||st=="{")node.removeChild(node.firstChild);}if(node.nodeName=="mrow"){st=node.lastChild.firstChild.nodeValue;if(st==")"||st=="]"||st=="}")node.removeChild(node.lastChild);}}var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol;function AMTgetTeXsymbol(symb){if(typeof symb.val=="boolean"&&symb.val){pre='';}else{pre='\\';}if(symb.tex==null){return(pre+symb.input);}else{return(pre+symb.tex);}}function AMTgetTeXbracket(symb){if(symb.tex==null){return(symb.input);}else{return('\\'+symb.tex);}}function AMTparseSexpr(str){var symbol,node,result,i,st,
newFrag='';str=AMremoveCharsAndBlanks(str,0);symbol=AMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET&&AMnestingDepth>0){return[null,str];}if(symbol.ttype==DEFINITION){str=symbol.output+AMremoveCharsAndBlanks(str,symbol.input.length);symbol=AMgetSymbol(str);}switch(symbol.ttype){case UNDEROVER:
case CONST:
str=AMremoveCharsAndBlanks(str,symbol.input.length);var texsymbol=AMTgetTeXsymbol(symbol);if(texsymbol.charAt(0)=="\\"||symbol.tag=="mo")return[texsymbol,str];else return['{'+texsymbol+'}',str];case LEFTBRACKET:
AMnestingDepth++;str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseExpr(str,true);AMnestingDepth--;if(typeof symbol.invisible=="boolean"&&symbol.invisible)
node='{\\left.'+result[0]+'}';else{node='{\\left'+AMTgetTeXbracket(symbol)+result[0]+'}';}return[node,result[1]];case TEXT:
if(symbol!=AMquote)str=AMremoveCharsAndBlanks(str,symbol.input.length);if(str.charAt(0)=="{")i=str.indexOf("}");else if(str.charAt(0)=="(")i=str.indexOf(")");else if(str.charAt(0)=="[")i=str.indexOf("]");else if(symbol==AMquote)i=str.slice(1).indexOf("\"")+1;else i=0;if(i==-1)i=str.length;st=str.slice(1,i);if(st.charAt(0)==" "){newFrag='\\ ';}newFrag+='\\text{'+st+'}';if(st.charAt(st.length-1)==" "){newFrag+='\\ ';}str=AMremoveCharsAndBlanks(str,i+1);return[newFrag,str];case UNARY:
str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseSexpr(str);if(result[0]==null)return['{'+AMTgetTeXsymbol(symbol)+'}',str];if(typeof symbol.func=="boolean"&&symbol.func){st=str.charAt(0);if(st=="^"||st=="_"||st=="/"||st=="|"||st==","){return['{'+AMTgetTeXsymbol(symbol)+'}',str];}else{node='{'+AMTgetTeXsymbol(symbol)+'{'+result[0]+'}}';return[node,result[1]];}}result[0]=AMTremoveBrackets(result[0]);if(symbol.input=="sqrt"){return['\\sqrt{'+result[0]+'}',result[1]];}else if(typeof symbol.acc=="boolean"&&symbol.acc){return['{'+AMTgetTeXsymbol(symbol)+'{'+result[0]+'}}',result[1]];}else{return['{'+AMTgetTeXsymbol(symbol)+'{'+result[0]+'}}',result[1]];}case BINARY:
str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseSexpr(str);if(result[0]==null)return['{'+AMTgetTeXsymbol(symbol)+'}',str];result[0]=AMTremoveBrackets(result[0]);var result2=AMTparseSexpr(result[1]);if(result2[0]==null)return['{'+AMTgetTeXsymbol(symbol)+'}',str];result2[0]=AMTremoveBrackets(result2[0]);if(symbol.input=="root"||symbol.input=="stackrel"){if(symbol.input=="root"){newFrag='{\\sqrt['+result[0]+']{'+result2[0]+'}}';}else{newFrag='{'+AMTgetTeXsymbol(symbol)+'{'+result[0]+'}{'+result2[0]+'}}';}}if(symbol.input=="frac"){newFrag='{\\frac{'+result[0]+'}{'+result2[0]+'}}';}return[newFrag,result2[1]];case INFIX:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return[symbol.output,str];case SPACE:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return['{\\quad\\text{'+symbol.input+'}\\quad}',str];case LEFTRIGHT:
AMnestingDepth++;str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseExpr(str,false);AMnestingDepth--;var st="";st=result[0].charAt(result[0].length-1);if(st=="|"){node='{\\left|'+result[0]+'}';return[node,result[1]];}else{node='{\\mid}';return[node,str];}default:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return['{'+AMTgetTeXsymbol(symbol)+'}',str];}}function AMTparseIexpr(str){var symbol,sym1,sym2,node,result,underover;str=AMremoveCharsAndBlanks(str,0);sym1=AMgetSymbol(str);result=AMTparseSexpr(str);node=result[0];str=result[1];symbol=AMgetSymbol(str);if(symbol.ttype==INFIX&&symbol.input!="/"){str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseSexpr(str);if(result[0]==null)
result[0]='{}';else result[0]=AMTremoveBrackets(result[0]);str=result[1];if(symbol.input=="_"){sym2=AMgetSymbol(str);underover=(sym1.ttype==UNDEROVER);if(sym2.input=="^"){str=AMremoveCharsAndBlanks(str,sym2.input.length);var res2=AMTparseSexpr(str);res2[0]=AMTremoveBrackets(res2[0]);str=res2[1];node='{'+node;node+='_{'+result[0]+'}';node+='^{'+res2[0]+'}';node+='}';}else{node+='_{'+result[0]+'}';}}else{node='{'+node+'}^{'+result[0]+'}';}}return[node,str];}function AMTparseExpr(str,rightbracket){var symbol,node,result,i,nodeList=[],
newFrag='';var addedright=false;do{str=AMremoveCharsAndBlanks(str,0);result=AMTparseIexpr(str);node=result[0];str=result[1];symbol=AMgetSymbol(str);if(symbol.ttype==INFIX&&symbol.input=="/"){str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMTparseIexpr(str);if(result[0]==null)
result[0]='{}';else result[0]=AMTremoveBrackets(result[0]);str=result[1];node=AMTremoveBrackets(node);node='\\frac'+'{'+node+'}';node+='{'+result[0]+'}';newFrag+=node;symbol=AMgetSymbol(str);}else if(node!=undefined)newFrag+=node;}while((symbol.ttype!=RIGHTBRACKET&&(symbol.ttype!=LEFTRIGHT||rightbracket)
||AMnestingDepth==0)&&symbol!=null&&symbol.output!="");if(symbol.ttype==RIGHTBRACKET||symbol.ttype==LEFTRIGHT){var len=newFrag.length;if(len>2&&newFrag.charAt(0)=='{'&&newFrag.indexOf(',')>0){var right=newFrag.charAt(len-2);if(right==')'||right==']'){var left=newFrag.charAt(6);if((left=='('&&right==')'&&symbol.output!='}')||(left=='['&&right==']')){var mxout='\\matrix{';var pos=new Array();pos.push(0);var matrix=true;var mxnestingd=0;for(i=1;i<len-1;i++){if(newFrag.charAt(i)==left)mxnestingd++;if(newFrag.charAt(i)==right){mxnestingd--;if(mxnestingd==0&&newFrag.charAt(i+2)==','&&newFrag.charAt(i+3)=='{')pos.push(i+2);}}pos.push(len);var lastmxsubcnt=-1;if(mxnestingd==0&&pos.length>0){for(i=0;i<pos.length-1;i++){if(i>0)mxout+='\\\\';if(i==0){var subarr=newFrag.substr(pos[i]+7,pos[i+1]-pos[i]-15).split(',');}else{var subarr=newFrag.substr(pos[i]+8,pos[i+1]-pos[i]-16).split(',');}if(lastmxsubcnt>0&&subarr.length!=lastmxsubcnt){matrix=false;}else if(lastmxsubcnt==-1){lastmxsubcnt=subarr.length;}mxout+=subarr.join('&');}}mxout+='}';if(matrix){newFrag=mxout;}}}}str=AMremoveCharsAndBlanks(str,symbol.input.length);if(typeof symbol.invisible!="boolean"||!symbol.invisible){node='\\right'+AMTgetTeXbracket(symbol);newFrag+=node;addedright=true;}else{newFrag+='\\right.';addedright=true;}}if(AMnestingDepth>0&&!addedright){newFrag+='\\right.';}return[newFrag,str];}function AMTparseAMtoTeX(str){AMnestingDepth=0;str=str.replace(/&nbsp;/g,"");str=str.replace(/&gt;/g,">");str=str.replace(/&lt;/g,"<");return AMTparseExpr(str.replace(/^\s+/g,""),false)[0];}function AMTparseMath(str){var texstring=AMTparseAMtoTeX(str);if(mathcolor!=""){texstring=texstring;}if(displaystyle){texstring="\\displaystyle"+texstring;}else{texstring="\\textstyle"+texstring;}var node=AMcreateElementXHTML("img");if(typeof encodeURIComponent=="function"){texstring=encodeURIComponent(texstring);}else{texstring=escape(texstring);}node.src=AMTcgiloc+'?'+'%5Ccolor{blue}'+texstring;node.style.verticalAlign="middle";if(showasciiformulaonhover)
node.setAttribute("title",str.replace(/\s+/g," "));return node;}function AMparseSexpr(str){var symbol,node,result,i,st,
newFrag=document.createDocumentFragment();str=AMremoveCharsAndBlanks(str,0);symbol=AMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET&&AMnestingDepth>0){return[null,str];}if(symbol.ttype==DEFINITION){str=symbol.output+AMremoveCharsAndBlanks(str,symbol.input.length);symbol=AMgetSymbol(str);}switch(symbol.ttype){case UNDEROVER:
case CONST:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return[AMcreateMmlNode(symbol.tag,
document.createTextNode(symbol.output)),str];case LEFTBRACKET:
AMnestingDepth++;str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseExpr(str,true);AMnestingDepth--;if(typeof symbol.invisible=="boolean"&&symbol.invisible)
node=AMcreateMmlNode("mrow",result[0]);else{node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));node=AMcreateMmlNode("mrow",node);node.appendChild(result[0]);}return[node,result[1]];case TEXT:
if(symbol!=AMquote)str=AMremoveCharsAndBlanks(str,symbol.input.length);if(str.charAt(0)=="{")i=str.indexOf("}");else if(str.charAt(0)=="(")i=str.indexOf(")");else if(str.charAt(0)=="[")i=str.indexOf("]");else if(symbol==AMquote)i=str.slice(1).indexOf("\"")+1;else i=0;if(i==-1)i=str.length;st=str.slice(1,i);if(st.charAt(0)==" "){node=AMcreateElementMathML("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);}newFrag.appendChild(
AMcreateMmlNode(symbol.tag,document.createTextNode(st)));if(st.charAt(st.length-1)==" "){node=AMcreateElementMathML("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);}str=AMremoveCharsAndBlanks(str,i+1);return[AMcreateMmlNode("mrow",newFrag),str];case UNARY:
str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseSexpr(str);if(result[0]==null)return[AMcreateMmlNode(symbol.tag,
document.createTextNode(symbol.output)),str];if(typeof symbol.func=="boolean"&&symbol.func){st=str.charAt(0);if(st=="^"||st=="_"||st=="/"||st=="|"||st==","){return[AMcreateMmlNode(symbol.tag,
document.createTextNode(symbol.output)),str];}else{node=AMcreateMmlNode("mrow",
AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)));node.appendChild(result[0]);return[node,result[1]];}}AMremoveBrackets(result[0]);if(symbol.input=="sqrt"){return[AMcreateMmlNode(symbol.tag,result[0]),result[1]];}else if(typeof symbol.acc=="boolean"&&symbol.acc){node=AMcreateMmlNode(symbol.tag,result[0]);node.appendChild(AMcreateMmlNode("mo",document.createTextNode(symbol.output)));return[node,result[1]];}else{if(!isIE&&typeof symbol.codes!="undefined"){for(i=0;i<result[0].childNodes.length;i++)
if(result[0].childNodes[i].nodeName=="mi"||result[0].nodeName=="mi"){st=(result[0].nodeName=="mi"?result[0].firstChild.nodeValue:
result[0].childNodes[i].firstChild.nodeValue);var newst=[];for(var j=0;j<st.length;j++)
if(st.charCodeAt(j)>64&&st.charCodeAt(j)<91)newst=newst+String.fromCharCode(symbol.codes[st.charCodeAt(j)-65]);else newst=newst+st.charAt(j);if(result[0].nodeName=="mi")
result[0]=AMcreateElementMathML("mo").
appendChild(document.createTextNode(newst));else result[0].replaceChild(AMcreateElementMathML("mo").
appendChild(document.createTextNode(newst)),result[0].childNodes[i]);}}node=AMcreateMmlNode(symbol.tag,result[0]);node.setAttribute(symbol.atname,symbol.atval);return[node,result[1]];}case BINARY:
str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseSexpr(str);if(result[0]==null)return[AMcreateMmlNode("mo",
document.createTextNode(symbol.input)),str];AMremoveBrackets(result[0]);var result2=AMparseSexpr(result[1]);if(result2[0]==null)return[AMcreateMmlNode("mo",
document.createTextNode(symbol.input)),str];AMremoveBrackets(result2[0]);if(symbol.input=="root"||symbol.input=="stackrel")
newFrag.appendChild(result2[0]);newFrag.appendChild(result[0]);if(symbol.input=="frac")newFrag.appendChild(result2[0]);return[AMcreateMmlNode(symbol.tag,newFrag),result2[1]];case INFIX:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return[AMcreateMmlNode("mo",document.createTextNode(symbol.output)),str];case SPACE:
str=AMremoveCharsAndBlanks(str,symbol.input.length);node=AMcreateElementMathML("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);newFrag.appendChild(
AMcreateMmlNode(symbol.tag,document.createTextNode(symbol.output)));node=AMcreateElementMathML("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);return[AMcreateMmlNode("mrow",newFrag),str];case LEFTRIGHT:
AMnestingDepth++;str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseExpr(str,false);AMnestingDepth--;var st="";if(result[0].lastChild!=null)
st=result[0].lastChild.firstChild.nodeValue;if(st=="|"){node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));node=AMcreateMmlNode("mrow",node);node.appendChild(result[0]);return[node,result[1]];}else{node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));node=AMcreateMmlNode("mrow",node);return[node,str];}default:
str=AMremoveCharsAndBlanks(str,symbol.input.length);return[AMcreateMmlNode(symbol.tag,
document.createTextNode(symbol.output)),str];}}function AMparseIexpr(str){var symbol,sym1,sym2,node,result,underover;str=AMremoveCharsAndBlanks(str,0);sym1=AMgetSymbol(str);result=AMparseSexpr(str);node=result[0];str=result[1];symbol=AMgetSymbol(str);if(symbol.ttype==INFIX&&symbol.input!="/"){str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseSexpr(str);if(result[0]==null)
result[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));else AMremoveBrackets(result[0]);str=result[1];if(symbol.input=="_"){sym2=AMgetSymbol(str);underover=(sym1.ttype==UNDEROVER);if(sym2.input=="^"){str=AMremoveCharsAndBlanks(str,sym2.input.length);var res2=AMparseSexpr(str);AMremoveBrackets(res2[0]);str=res2[1];node=AMcreateMmlNode((underover?"munderover":"msubsup"),node);node.appendChild(result[0]);node.appendChild(res2[0]);node=AMcreateMmlNode("mrow",node);}else{node=AMcreateMmlNode((underover?"munder":"msub"),node);node.appendChild(result[0]);}}else{node=AMcreateMmlNode(symbol.tag,node);node.appendChild(result[0]);}}return[node,str];}function AMparseExpr(str,rightbracket){var symbol,node,result,i,nodeList=[],
newFrag=document.createDocumentFragment();do{str=AMremoveCharsAndBlanks(str,0);result=AMparseIexpr(str);node=result[0];str=result[1];symbol=AMgetSymbol(str);if(symbol.ttype==INFIX&&symbol.input=="/"){str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseIexpr(str);if(result[0]==null)
result[0]=AMcreateMmlNode("mo",document.createTextNode("\u25A1"));else AMremoveBrackets(result[0]);str=result[1];AMremoveBrackets(node);node=AMcreateMmlNode(symbol.tag,node);node.appendChild(result[0]);newFrag.appendChild(node);symbol=AMgetSymbol(str);}else if(node!=undefined)newFrag.appendChild(node);}while((symbol.ttype!=RIGHTBRACKET&&(symbol.ttype!=LEFTRIGHT||rightbracket)
||AMnestingDepth==0)&&symbol!=null&&symbol.output!="");if(symbol.ttype==RIGHTBRACKET||symbol.ttype==LEFTRIGHT){var len=newFrag.childNodes.length;if(len>0&&newFrag.childNodes[len-1].nodeName=="mrow"&&len>1&&newFrag.childNodes[len-2].nodeName=="mo"&&newFrag.childNodes[len-2].firstChild.nodeValue==","){var right=newFrag.childNodes[len-1].lastChild.firstChild.nodeValue;if(right==")"||right=="]"){var left=newFrag.childNodes[len-1].firstChild.firstChild.nodeValue;if(left=="("&&right==")"&&symbol.output!="}"||left=="["&&right=="]"){var pos=[];var matrix=true;var m=newFrag.childNodes.length;for(i=0;matrix&&i<m;i=i+2){pos[i]=[];node=newFrag.childNodes[i];if(matrix)matrix=node.nodeName=="mrow"&&(i==m-1||node.nextSibling.nodeName=="mo"&&node.nextSibling.firstChild.nodeValue==",")&&node.firstChild.firstChild.nodeValue==left&&node.lastChild.firstChild.nodeValue==right;if(matrix)
for(var j=0;j<node.childNodes.length;j++)
if(node.childNodes[j].firstChild.nodeValue==",")
pos[i][pos[i].length]=j;if(matrix&&i>1)matrix=pos[i].length==pos[i-2].length;}if(matrix){var row,frag,n,k,table=document.createDocumentFragment();for(i=0;i<m;i=i+2){row=document.createDocumentFragment();frag=document.createDocumentFragment();node=newFrag.firstChild;n=node.childNodes.length;k=0;node.removeChild(node.firstChild);for(j=1;j<n-1;j++){if(typeof pos[i][k]!="undefined"&&j==pos[i][k]){node.removeChild(node.firstChild);row.appendChild(AMcreateMmlNode("mtd",frag));k++;}else frag.appendChild(node.firstChild);}row.appendChild(AMcreateMmlNode("mtd",frag));if(newFrag.childNodes.length>2){newFrag.removeChild(newFrag.firstChild);newFrag.removeChild(newFrag.firstChild);}table.appendChild(AMcreateMmlNode("mtr",row));}node=AMcreateMmlNode("mtable",table);if(typeof symbol.invisible=="boolean"&&symbol.invisible)node.setAttribute("columnalign","left");newFrag.replaceChild(node,newFrag.firstChild);}}}}str=AMremoveCharsAndBlanks(str,symbol.input.length);if(typeof symbol.invisible!="boolean"||!symbol.invisible){node=AMcreateMmlNode("mo",document.createTextNode(symbol.output));newFrag.appendChild(node);}}return[newFrag,str];}function AMparseMath(str){var result,node=AMcreateElementMathML("mstyle");if(mathcolor!="")node.setAttribute("mathcolor",mathcolor);if(displaystyle)node.setAttribute("displaystyle","true");if(mathfontfamily!="")node.setAttribute("fontfamily",mathfontfamily);AMnestingDepth=0;str=str.replace(/&nbsp;/g,"");str=str.replace(/&gt;/g,">");str=str.replace(/&lt;/g,"<");node.appendChild(AMparseExpr(str.replace(/^\s+/g,""),false)[0]);node=AMcreateMmlNode("math",node);if(showasciiformulaonhover)
node.setAttribute("title",str.replace(/\s+/g," "));if(mathfontfamily!=""&&(isIE||mathfontfamily!="serif")){var fnode=AMcreateElementXHTML("font");fnode.setAttribute("face",mathfontfamily);fnode.appendChild(node);return fnode;}return node;}function AMstrarr2docFrag(arr,linebreaks,usingMathML){var newFrag=document.createDocumentFragment();var expr=false;for(var i=0;i<arr.length;i++){if(expr&&!usingMathML)newFrag.appendChild(AMTparseMath(arr[i]));else if(expr&&usingMathML)newFrag.appendChild(AMparseMath(arr[i]));else{var arri=(linebreaks?arr[i].split("\n\n"):[arr[i]]);newFrag.appendChild(AMcreateElementXHTML("span").
appendChild(document.createTextNode(arri[0])));for(var j=1;j<arri.length;j++){newFrag.appendChild(AMcreateElementXHTML("p"));newFrag.appendChild(AMcreateElementXHTML("span").
appendChild(document.createTextNode(arri[j])));}}expr=!expr;}return newFrag;}function AMprocessNodeR(n,linebreaks){var mtch,str,arr,frg,i;if(n.childNodes.length==0){if((n.nodeType!=8||linebreaks)&&n.parentNode.nodeName!="form"&&n.parentNode.nodeName!="FORM"&&n.parentNode.nodeName!="textarea"&&n.parentNode.nodeName!="TEXTAREA"&&n.parentNode.nodeName!="pre"&&n.parentNode.nodeName!="PRE"){str=n.nodeValue;if(!(str==null)){str=str.replace(/\r\n\r\n/g,"\n\n");if(doubleblankmathdelimiter){str=str.replace(/\x20\x20\./g," "+AMdelimiter1+".");str=str.replace(/\x20\x20,/g," "+AMdelimiter1+",");str=str.replace(/\x20\x20/g," "+AMdelimiter1+" ");}str=str.replace(/\x20+/g," ");str=str.replace(/\s*\r\n/g," ");mtch=false;if(AMusedelimiter2){str=str.replace(new RegExp(AMescape2,"g"),
function(st){mtch=true;return"AMescape2"});}str=str.replace(new RegExp(AMescape1,"g"),
function(st){mtch=true;return"AMescape1"});if(AMusedelimiter2)str=str.replace(new RegExp(AMdelimiter2regexp,"g"),AMdelimiter1);arr=str.split(AMdelimiter1);for(i=0;i<arr.length;i++)
if(AMusedelimiter2){arr[i]=arr[i].replace(/AMescape2/g,AMdelimiter2).replace(/AMescape1/g,AMdelimiter1);}if(arr.length>1||mtch){if(checkForMathML){checkForMathML=false;var nd=AMisMathMLavailable();AMnoMathML=nd!=null;if(AMnoMathML&&notifyIfNoMathML)
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(nd,AMbody.childNodes[0]);}if(!AMnoMathML){frg=AMstrarr2docFrag(arr,n.nodeType==8,true);}else{frg=AMstrarr2docFrag(arr,n.nodeType==8,false);}var len=frg.childNodes.length;n.parentNode.replaceChild(frg,n);return len-1;}}}else return 0;}else if(n.nodeName!="math"){for(i=0;i<n.childNodes.length;i++)
i+=AMprocessNodeR(n.childNodes[i],linebreaks);}return 0;}function AMprocessNode(n,linebreaks,spanclassAM){var frag,st;if(spanclassAM!=null){;frag=document.getElementsByTagName("span")
for(var i=0;i<frag.length;i++)
if(frag[i].className=="AM")
AMprocessNodeR(frag[i],linebreaks);}else{try{st=n.innerHTML;}catch(err){}if(AMusedelimiter2){if(st==null||st.indexOf(AMdelimiter1)!=-1||st.indexOf(AMdelimiter2)!=-1)
AMprocessNodeR(n,linebreaks);}else{if(st==null||st.indexOf(AMdelimiter1)!=-1)
AMprocessNodeR(n,linebreaks);}}if(isIE){frag=document.getElementsByTagName('math');for(var i=0;i<frag.length;i++)frag[i].update()
}}var AMbody;var AMnoMathML=false,AMtranslated=false;function translate(spanclassAM){if(!AMtranslated){AMtranslated=true;AMinitSymbols();AMbody=document.getElementsByTagName("body")[0];AMprocessNode(AMbody,false,spanclassAM);}}if(isIE){document.write("<object id=\"mathplayer\"\
	classid=\"clsid:32F66A20-7614-11D4-BD11-00104BD3F987\"></object>");document.write("<?import namespace=\"m\" implementation=\"#mathplayer\"?>");}function generic()
{if(-1!=self.location.href.indexOf("spaces."))translate();};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;}}if(checkForMathML){checkForMathML=false;var nd=AMisMathMLavailable();AMnoMathML=nd!=null;}