function AMcreateElementXHTML(t){return AMnoNS?document.createElement(t):document.createElementNS("http://www.w3.org/1999/xhtml",t)}function AMnoMathMLNote(){var t=AMcreateElementXHTML("h3");t.setAttribute("align","center"),t.appendChild(AMcreateElementXHTML("p")),t.appendChild(document.createTextNode("To view the "));var e=AMcreateElementXHTML("a");return e.appendChild(document.createTextNode("ASCIIMathML")),e.setAttribute("href","http://www.chapman.edu/~jipsen/asciimath.html"),t.appendChild(e),t.appendChild(document.createTextNode(" notation use Internet Explorer 6+")),e=AMcreateElementXHTML("a"),e.appendChild(document.createTextNode("MathPlayer")),e.setAttribute("href","http://www.dessci.com/en/products/mathplayer/download.htm"),t.appendChild(e),t.appendChild(document.createTextNode(" or Netscape/Mozilla/Firefox")),t.appendChild(AMcreateElementXHTML("p")),t}function AMisMathMLavailable(){if(navigator.product&&"Gecko"==navigator.product){var t=navigator.userAgent.toLowerCase().match(/rv:\s*([\d\.]+)/);return null!=t&&(t=t[1].split("."),t.length<3&&(t[2]=0),t.length<2&&(t[1]=0)),null!=t&&1e4*t[0]+100*t[1]+1*t[2]>=10100?(AMisGecko=1e4*t[0]+100*t[1]+1*t[2],null):AMnoMathMLNote()}if("Microsoft"!=navigator.appName.slice(0,9))return AMnoMathMLNote();try{{new ActiveXObject("MathPlayer.Factory.1")}return null}catch(e){return AMnoMathMLNote()}}function compareNames(t,e){return t.input>e.input?1:-1}function AMinitSymbols(){var t,e=[];for(t=0;t<AMsymbols.length;t++)!AMsymbols[t].tex||"boolean"==typeof AMsymbols[t].notexcopy&&AMsymbols[t].notexcopy||(e[e.length]={input:AMsymbols[t].tex,tag:AMsymbols[t].tag,output:AMsymbols[t].output,ttype:AMsymbols[t].ttype});for(AMsymbols=AMsymbols.concat(e),AMsymbols.sort(compareNames),t=0;t<AMsymbols.length;t++)AMnames[t]=AMsymbols[t].input}function AMcreateElementMathML(t){return AMisIE?document.createElement("m:"+t):document.createElementNS(AMmathml,t)}function AMcreateMmlNode(t,e){if(AMisIE)var n=document.createElement("m:"+t);else var n=document.createElementNS(AMmathml,t);return n.appendChild(e),n}function newcommand(t,e){AMsymbols=AMsymbols.concat([{input:t,tag:"mo",output:e,tex:null,ttype:DEFINITION}])}function AMremoveCharsAndBlanks(t,e){var n;n=t.slice("\\"==t.charAt(e)&&"\\"!=t.charAt(e+1)&&" "!=t.charAt(e+1)?e+1:e);for(var u=0;u<n.length&&n.charCodeAt(u)<=32;u+=1);return n.slice(u)}function AMposition(t,e,n){if(0==n){var u,o;for(n=-1,u=t.length;u>n+1;)o=n+u>>1,t[o]<e?n=o:u=o;return u}for(var a=n;a<t.length&&t[a]<e;a++);return a}function AMgetSymbol(t){for(var e,n,u,o=0,a=0,p="",l=!0,i=1;i<=t.length&&l;i++)n=t.slice(0,i),a=o,o=AMposition(AMnames,n,a),o<AMnames.length&&t.slice(0,AMnames[o].length)==AMnames[o]&&(p=AMnames[o],e=o,i=p.length),l=o<AMnames.length&&t.slice(0,AMnames[o].length)>=AMnames[o];if(AMpreviousSymbol=AMcurrentSymbol,""!=p)return AMcurrentSymbol=AMsymbols[e].ttype,AMsymbols[e];AMcurrentSymbol=CONST,o=1,n=t.slice(0,1);for(var r=!0;n>="0"&&"9">=n&&o<=t.length;)n=t.slice(o,o+1),o++;if(n==decimalsign&&(n=t.slice(o,o+1),n>="0"&&"9">=n))for(r=!1,o++;n>="0"&&"9">=n&&o<=t.length;)n=t.slice(o,o+1),o++;return r&&o>1||o>2?(n=t.slice(0,o-1),u="mn"):(o=2,n=t.slice(0,1),u=("A">n||n>"Z")&&("a">n||n>"z")?"mo":"mi"),"-"==n&&AMpreviousSymbol==INFIX?(AMcurrentSymbol=INFIX,{input:n,tag:u,output:n,ttype:UNARY,func:!0,val:!0}):{input:n,tag:u,output:n,ttype:CONST,val:!0}}function AMTremoveBrackets(t){var e;return"{"==t.charAt(0)&&"}"==t.charAt(t.length-1)&&(e=t.charAt(1),("("==e||"["==e)&&(t="{"+t.substr(2)),e=t.substr(1,6),("\\left("==e||"\\left["==e||"\\left{"==e)&&(t="{"+t.substr(7)),e=t.substr(1,12),("\\left\\lbrace"==e||"\\left\\langle"==e)&&(t="{"+t.substr(13)),e=t.charAt(t.length-2),(")"==e||"]"==e||"."==e)&&(t=t.substr(0,t.length-8)+"}"),e=t.substr(t.length-8,7),("\\rbrace"==e||"\\rangle"==e)&&(t=t.substr(0,t.length-14)+"}")),t}function AMremoveBrackets(t){var e;("mrow"==t.nodeName||"M:MROW"==t.nodeName)&&(e=t.firstChild.firstChild.nodeValue,("("==e||"["==e||"{"==e)&&t.removeChild(t.firstChild)),("mrow"==t.nodeName||"M:MROW"==t.nodeName)&&(e=t.lastChild.firstChild.nodeValue,(")"==e||"]"==e||"}"==e)&&t.removeChild(t.lastChild))}function AMTgetTeXsymbol(t){return pre="boolean"==typeof t.val&&t.val?"":"\\",null==t.tex?pre+(""==pre?t.input:t.input.toLowerCase()):pre+t.tex}function AMTgetTeXbracket(t){return null==t.tex?t.input:"\\"+t.tex}function AMTparseSexpr(t){var e,n,u,o,a,p="";if(t=AMremoveCharsAndBlanks(t,0),e=AMgetSymbol(t),null==e||e.ttype==RIGHTBRACKET&&AMnestingDepth>0)return[null,t];switch(e.ttype==DEFINITION&&(t=e.output+AMremoveCharsAndBlanks(t,e.input.length),e=AMgetSymbol(t)),e.ttype){case UNDEROVER:case CONST:t=AMremoveCharsAndBlanks(t,e.input.length);var l=AMTgetTeXsymbol(e);return"\\"==l.charAt(0)||"mo"==e.tag?[l,t]:["{"+l+"}",t];case LEFTBRACKET:return AMnestingDepth++,t=AMremoveCharsAndBlanks(t,e.input.length),u=AMTparseExpr(t,!0),AMnestingDepth--,"\\right"==u[0].substr(0,6)?(u[0]=u[0].substr("\\right."==u[0].substr(0,7)?7:6),n="boolean"==typeof e.invisible&&e.invisible?"{"+u[0]+"}":"{"+AMTgetTeXbracket(e)+u[0]+"}"):n="boolean"==typeof e.invisible&&e.invisible?"{\\left."+u[0]+"}":"{\\left"+AMTgetTeXbracket(e)+u[0]+"}",[n,u[1]];case TEXT:return e!=AMquote&&(t=AMremoveCharsAndBlanks(t,e.input.length)),o="{"==t.charAt(0)?t.indexOf("}"):"("==t.charAt(0)?t.indexOf(")"):"["==t.charAt(0)?t.indexOf("]"):e==AMquote?t.slice(1).indexOf('"')+1:0,-1==o&&(o=t.length),a=t.slice(1,o)," "==a.charAt(0)&&(p="\\ "),p+="\\text{"+a+"}"," "==a.charAt(a.length-1)&&(p+="\\ "),t=AMremoveCharsAndBlanks(t,o+1),[p,t];case UNARY:return t=AMremoveCharsAndBlanks(t,e.input.length),u=AMTparseSexpr(t),null==u[0]?["{"+AMTgetTeXsymbol(e)+"}",t]:"boolean"==typeof e.func&&e.func?(a=t.charAt(0),"^"==a||"_"==a||"/"==a||"|"==a||","==a?["{"+AMTgetTeXsymbol(e)+"}",t]:(n="{"+AMTgetTeXsymbol(e)+"{"+u[0]+"}}",[n,u[1]])):(u[0]=AMTremoveBrackets(u[0]),"sqrt"==e.input?["\\sqrt{"+u[0]+"}",u[1]]:"boolean"==typeof e.acc&&e.acc?["{"+AMTgetTeXsymbol(e)+"{"+u[0]+"}}",u[1]]:["{"+AMTgetTeXsymbol(e)+"{"+u[0]+"}}",u[1]]);case BINARY:if(t=AMremoveCharsAndBlanks(t,e.input.length),u=AMTparseSexpr(t),null==u[0])return["{"+AMTgetTeXsymbol(e)+"}",t];u[0]=AMTremoveBrackets(u[0]);var i=AMTparseSexpr(u[1]);return null==i[0]?["{"+AMTgetTeXsymbol(e)+"}",t]:(i[0]=AMTremoveBrackets(i[0]),"color"==e.input&&(p="{\\color{"+u[0].replace(/[\{\}]/g,"")+"}"+i[0]+"}}"),("root"==e.input||"stackrel"==e.input)&&(p="root"==e.input?"{\\sqrt["+u[0]+"]{"+i[0]+"}}":"{"+AMTgetTeXsymbol(e)+"{"+u[0]+"}{"+i[0]+"}}"),"frac"==e.input&&(p="{\\frac{"+u[0]+"}{"+i[0]+"}}"),[p,i[1]]);case INFIX:return t=AMremoveCharsAndBlanks(t,e.input.length),[e.output,t];case SPACE:return t=AMremoveCharsAndBlanks(t,e.input.length),["{\\quad\\text{"+e.input+"}\\quad}",t];case LEFTRIGHT:AMnestingDepth++,t=AMremoveCharsAndBlanks(t,e.input.length),u=AMTparseExpr(t,!1),AMnestingDepth--;var a="";return a=u[0].charAt(u[0].length-1),"|"==a?(n="{\\left|"+u[0]+"}",[n,u[1]]):(n="{\\mid}",[n,t]);default:return t=AMremoveCharsAndBlanks(t,e.input.length),["{"+AMTgetTeXsymbol(e)+"}",t]}}function AMTparseIexpr(t){var e,n,u,o,a,p;if(t=AMremoveCharsAndBlanks(t,0),n=AMgetSymbol(t),a=AMTparseSexpr(t),o=a[0],t=a[1],e=AMgetSymbol(t),e.ttype==INFIX&&"/"!=e.input)if(t=AMremoveCharsAndBlanks(t,e.input.length),a=AMTparseSexpr(t),a[0]=null==a[0]?"{}":AMTremoveBrackets(a[0]),t=a[1],"_"==e.input)if(u=AMgetSymbol(t),p=n.ttype==UNDEROVER,"^"==u.input){t=AMremoveCharsAndBlanks(t,u.input.length);var l=AMTparseSexpr(t);l[0]=AMTremoveBrackets(l[0]),t=l[1],o="{"+o,o+="_{"+a[0]+"}",o+="^{"+l[0]+"}",o+="}"}else o+="_{"+a[0]+"}";else o="{"+o+"}^{"+a[0]+"}";return[o,t]}function AMTparseExpr(t,e){var n,u,o,a,p="",l=!1;do t=AMremoveCharsAndBlanks(t,0),o=AMTparseIexpr(t),u=o[0],t=o[1],n=AMgetSymbol(t),n.ttype==INFIX&&"/"==n.input?(t=AMremoveCharsAndBlanks(t,n.input.length),o=AMTparseIexpr(t),o[0]=null==o[0]?"{}":AMTremoveBrackets(o[0]),t=o[1],u=AMTremoveBrackets(u),u="\\frac{"+u+"}",u+="{"+o[0]+"}",p+=u,n=AMgetSymbol(t)):void 0!=u&&(p+=u);while((n.ttype!=RIGHTBRACKET&&(n.ttype!=LEFTRIGHT||e)||0==AMnestingDepth)&&null!=n&&""!=n.output);if(n.ttype==RIGHTBRACKET||n.ttype==LEFTRIGHT){var i=p.length;if(i>2&&"{"==p.charAt(0)&&p.indexOf(",")>0){var r=p.charAt(i-2);if(")"==r||"]"==r){var m=p.charAt(6);if("("==m&&")"==r&&"}"!=n.output||"["==m&&"]"==r){var s="\\matrix{",c=new Array;c.push(0);var d=!0,A=0,g=[];g[0]=[0];var h=0,M=0;for(a=1;i-1>a;a++)p.charAt(a)==m&&A++,p.charAt(a)==r&&(A--,0==A&&","==p.charAt(a+2)&&"{"==p.charAt(a+3)&&(c.push(a+2),h=a+2,g[h]=[a+2])),("["==p.charAt(a)||"("==p.charAt(a))&&M++,("]"==p.charAt(a)||")"==p.charAt(a))&&M--,","==p.charAt(a)&&1==M&&g[h].push(a);c.push(i);var y=-1;if(0==A&&c.length>0)for(a=0;a<c.length-1;a++){if(a>0&&(s+="\\\\"),0==a)if(1==g[c[a]].length)var N=[p.substr(c[a]+7,c[a+1]-c[a]-15)];else{for(var N=[p.substring(c[a]+7,g[c[a]][1])],x=2;x<g[c[a]].length;x++)N.push(p.substring(g[c[a]][x-1]+1,g[c[a]][x]));N.push(p.substring(g[c[a]][g[c[a]].length-1]+1,c[a+1]-8))}else if(1==g[c[a]].length)var N=[p.substr(c[a]+8,c[a+1]-c[a]-16)];else{for(var N=[p.substring(c[a]+8,g[c[a]][1])],x=2;x<g[c[a]].length;x++)N.push(p.substring(g[c[a]][x-1]+1,g[c[a]][x]));N.push(p.substring(g[c[a]][g[c[a]].length-1]+1,c[a+1]-8))}y>0&&N.length!=y?d=!1:-1==y&&(y=N.length),s+=N.join("&")}s+="}",d&&(p=s)}}}t=AMremoveCharsAndBlanks(t,n.input.length),"boolean"==typeof n.invisible&&n.invisible?(p+="\\right.",l=!0):(u="\\right"+AMTgetTeXbracket(n),p+=u,l=!0)}return AMnestingDepth>0&&!l&&(p+="\\right."),[p,t]}function AMTparseAMtoTeX(t){return AMnestingDepth=0,t=t.replace(/(&nbsp;|\u00a0|&#160;)/g,""),t=t.replace(/&gt;/g,">"),t=t.replace(/&lt;/g,"<"),null==t.match(/\S/)?"":AMTparseExpr(t.replace(/^\s+/g,""),!1)[0]}function AMTparseMath(t){if(-1!=t.indexOf("title")){var e=document.getElementById("fakeDiv");e.innerHTML=t;var n=document.getElementById("fakeDiv"),u=n.firstChild;t=u.getAttribute("title")}if(t=t.replace(/(&nbsp;|\u00a0|&#160;)/g,""),t=t.replace(/&gt;/g,">"),t=t.replace(/&lt;/g,"<"),null==t.match(/\S/))return document.createTextNode(" ");var o=AMTparseAMtoTeX(t);"undefined"!=typeof mathbg&&"dark"==mathbg&&(o="\\reverse "+o),""!=mathcolor&&(o="\\"+mathcolor+o),o=displaystyle?"\\displaystyle"+o:"\\textstyle"+o,o=o.replace("$","\\$");var a=AMcreateElementXHTML("img");return o="function"==typeof encodeURIComponent?encodeURIComponent(o):escape(o),a.src=AMTcgiloc+"?"+o,a.style.verticalAlign="middle",showasciiformulaonhover&&a.setAttribute("title",t.replace(/\s+/g," ")),a}function AMparseSexpr(t){var e,n,u,o,a,p=document.createDocumentFragment();if(t=AMremoveCharsAndBlanks(t,0),e=AMgetSymbol(t),null==e||e.ttype==RIGHTBRACKET&&AMnestingDepth>0)return[null,t];switch(e.ttype==DEFINITION&&(t=e.output+AMremoveCharsAndBlanks(t,e.input.length),e=AMgetSymbol(t)),e.ttype){case UNDEROVER:case CONST:return t=AMremoveCharsAndBlanks(t,e.input.length),[AMcreateMmlNode(e.tag,document.createTextNode(e.output)),t];case LEFTBRACKET:return AMnestingDepth++,t=AMremoveCharsAndBlanks(t,e.input.length),u=AMparseExpr(t,!0),AMnestingDepth--,"boolean"==typeof e.invisible&&e.invisible?n=AMcreateMmlNode("mrow",u[0]):(n=AMcreateMmlNode("mo",document.createTextNode(e.output)),n=AMcreateMmlNode("mrow",n),n.appendChild(u[0])),[n,u[1]];case TEXT:return e!=AMquote&&(t=AMremoveCharsAndBlanks(t,e.input.length)),o="{"==t.charAt(0)?t.indexOf("}"):"("==t.charAt(0)?t.indexOf(")"):"["==t.charAt(0)?t.indexOf("]"):e==AMquote?t.slice(1).indexOf('"')+1:0,-1==o&&(o=t.length),a=t.slice(1,o)," "==a.charAt(0)&&(n=AMcreateElementMathML("mspace"),n.setAttribute("width","1ex"),p.appendChild(n)),p.appendChild(AMcreateMmlNode(e.tag,document.createTextNode(a)))," "==a.charAt(a.length-1)&&(n=AMcreateElementMathML("mspace"),n.setAttribute("width","1ex"),p.appendChild(n)),t=AMremoveCharsAndBlanks(t,o+1),[AMcreateMmlNode("mrow",p),t];case UNARY:if(t=AMremoveCharsAndBlanks(t,e.input.length),u=AMparseSexpr(t),null==u[0])return[AMcreateMmlNode(e.tag,document.createTextNode(e.output)),t];if("boolean"==typeof e.func&&e.func)return a=t.charAt(0),"^"==a||"_"==a||"/"==a||"|"==a||","==a?[AMcreateMmlNode(e.tag,document.createTextNode(e.output)),t]:(n=AMcreateMmlNode("mrow",AMcreateMmlNode(e.tag,document.createTextNode(e.output))),n.appendChild(u[0]),[n,u[1]]);if(AMremoveBrackets(u[0]),"sqrt"==e.input)return[AMcreateMmlNode(e.tag,u[0]),u[1]];if("boolean"==typeof e.acc&&e.acc)return n=AMcreateMmlNode(e.tag,u[0]),n.appendChild(AMcreateMmlNode("mo",document.createTextNode(e.output))),[n,u[1]];if(!AMisIE&&"undefined"!=typeof e.codes)for(o=0;o<u[0].childNodes.length;o++)if("mi"==u[0].childNodes[o].nodeName||"mi"==u[0].nodeName){a="mi"==u[0].nodeName?u[0].firstChild.nodeValue:u[0].childNodes[o].firstChild.nodeValue;for(var l=[],i=0;i<a.length;i++)l+=a.charCodeAt(i)>64&&a.charCodeAt(i)<91?String.fromCharCode(e.codes[a.charCodeAt(i)-65]):a.charAt(i);"mi"==u[0].nodeName?u[0]=AMcreateElementMathML("mo").appendChild(document.createTextNode(l)):u[0].replaceChild(AMcreateElementMathML("mo").appendChild(document.createTextNode(l)),u[0].childNodes[o])}return n=AMcreateMmlNode(e.tag,u[0]),n.setAttribute(e.atname,e.atval),[n,u[1]];case BINARY:if(t=AMremoveCharsAndBlanks(t,e.input.length),u=AMparseSexpr(t),null==u[0])return[AMcreateMmlNode("mo",document.createTextNode(e.input)),t];AMremoveBrackets(u[0]);var r=AMparseSexpr(u[1]);return null==r[0]?[AMcreateMmlNode("mo",document.createTextNode(e.input)),t]:(AMremoveBrackets(r[0]),"color"==e.input?("{"==t.charAt(0)?o=t.indexOf("}"):"("==t.charAt(0)?o=t.indexOf(")"):"["==t.charAt(0)&&(o=t.indexOf("]")),a=t.slice(1,o),n=AMcreateMmlNode(e.tag,r[0]),n.setAttribute("color",a),[n,r[1]]):(("root"==e.input||"stackrel"==e.input)&&p.appendChild(r[0]),p.appendChild(u[0]),"frac"==e.input&&p.appendChild(r[0]),[AMcreateMmlNode(e.tag,p),r[1]]));case INFIX:return t=AMremoveCharsAndBlanks(t,e.input.length),[AMcreateMmlNode("mo",document.createTextNode(e.output)),t];case SPACE:return t=AMremoveCharsAndBlanks(t,e.input.length),n=AMcreateElementMathML("mspace"),n.setAttribute("width","1ex"),p.appendChild(n),p.appendChild(AMcreateMmlNode(e.tag,document.createTextNode(e.output))),n=AMcreateElementMathML("mspace"),n.setAttribute("width","1ex"),p.appendChild(n),[AMcreateMmlNode("mrow",p),t];case LEFTRIGHT:AMnestingDepth++,t=AMremoveCharsAndBlanks(t,e.input.length),u=AMparseExpr(t,!1),AMnestingDepth--;var a="";return null!=u[0].lastChild&&(a=u[0].lastChild.firstChild.nodeValue),"|"==a?(n=AMcreateMmlNode("mo",document.createTextNode(e.output)),n=AMcreateMmlNode("mrow",n),n.appendChild(u[0]),[n,u[1]]):(n=AMcreateMmlNode("mo",document.createTextNode(e.output)),n=AMcreateMmlNode("mrow",n),[n,t]);default:return t=AMremoveCharsAndBlanks(t,e.input.length),[AMcreateMmlNode(e.tag,document.createTextNode(e.output)),t]}}function AMparseIexpr(t){var e,n,u,o,a,p;if(t=AMremoveCharsAndBlanks(t,0),n=AMgetSymbol(t),a=AMparseSexpr(t),o=a[0],t=a[1],e=AMgetSymbol(t),e.ttype==INFIX&&"/"!=e.input)if(t=AMremoveCharsAndBlanks(t,e.input.length),a=AMparseSexpr(t),null==a[0]?a[0]=AMcreateMmlNode("mo",document.createTextNode("□")):AMremoveBrackets(a[0]),t=a[1],"_"==e.input)if(u=AMgetSymbol(t),p=n.ttype==UNDEROVER,"^"==u.input){t=AMremoveCharsAndBlanks(t,u.input.length);var l=AMparseSexpr(t);AMremoveBrackets(l[0]),t=l[1],o=AMcreateMmlNode(p?"munderover":"msubsup",o),o.appendChild(a[0]),o.appendChild(l[0]),o=AMcreateMmlNode("mrow",o)}else o=AMcreateMmlNode(p?"munder":"msub",o),o.appendChild(a[0]);else o=AMcreateMmlNode(e.tag,o),o.appendChild(a[0]);return[o,t]}function AMparseExpr(t,e){var n,u,o,a,p=document.createDocumentFragment();do t=AMremoveCharsAndBlanks(t,0),o=AMparseIexpr(t),u=o[0],t=o[1],n=AMgetSymbol(t),n.ttype==INFIX&&"/"==n.input?(t=AMremoveCharsAndBlanks(t,n.input.length),o=AMparseIexpr(t),null==o[0]?o[0]=AMcreateMmlNode("mo",document.createTextNode("□")):AMremoveBrackets(o[0]),t=o[1],AMremoveBrackets(u),u=AMcreateMmlNode(n.tag,u),u.appendChild(o[0]),p.appendChild(u),n=AMgetSymbol(t)):void 0!=u&&p.appendChild(u);while((n.ttype!=RIGHTBRACKET&&(n.ttype!=LEFTRIGHT||e)||0==AMnestingDepth)&&null!=n&&""!=n.output);if(n.ttype==RIGHTBRACKET||n.ttype==LEFTRIGHT){var 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