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if(st=="-"&&AMpreviousSymbol==INFIX){AMcurrentSymbol=INFIX;return{input:st,tag:tagst,output:st,ttype:UNARY,func:true};}
return{input:st,tag:tagst,output:st,ttype:CONST};}
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 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[createMmlNode(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=createMmlNode("mrow",result[0]);else{node=createMmlNode("mo",document.createTextNode(symbol.output));node=createMmlNode("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=createMmlNode("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);}
newFrag.appendChild(createMmlNode(symbol.tag,document.createTextNode(st)));if(st.charAt(st.length-1)==" "){node=createMmlNode("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);}
str=AMremoveCharsAndBlanks(str,i+1);return[createMmlNode("mrow",newFrag),str];case UNARY:str=AMremoveCharsAndBlanks(str,symbol.input.length);result=AMparseSexpr(str);if(result[0]==null)return[createMmlNode(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[createMmlNode(symbol.tag,document.createTextNode(symbol.output)),str];}else{node=createMmlNode("mrow",createMmlNode(symbol.tag,document.createTextNode(symbol.output)));node.appendChild(result[0]);return[node,result[1]];}}
AMremoveBrackets(result[0]);if(symbol.input=="sqrt"){return[createMmlNode(symbol.tag,result[0]),result[1]];}else if(typeof symbol.acc=="boolean"&&symbol.acc){node=createMmlNode(symbol.tag,result[0]);node.appendChild(createMmlNode("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]=createMmlNode("mo").appendChild(document.createTextNode(newst));else result[0].replaceChild(createMmlNode("mo").appendChild(document.createTextNode(newst)),result[0].childNodes[i]);}}
node=createMmlNode(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[createMmlNode("mo",document.createTextNode(symbol.input)),str];AMremoveBrackets(result[0]);var result2=AMparseSexpr(result[1]);if(result2[0]==null)return[createMmlNode("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[createMmlNode(symbol.tag,newFrag),result2[1]];case INFIX:str=AMremoveCharsAndBlanks(str,symbol.input.length);return[createMmlNode("mo",document.createTextNode(symbol.output)),str];case SPACE:str=AMremoveCharsAndBlanks(str,symbol.input.length);node=createMmlNode("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);newFrag.appendChild(createMmlNode(symbol.tag,document.createTextNode(symbol.output)));node=createMmlNode("mspace");node.setAttribute("width","1ex");newFrag.appendChild(node);return[createMmlNode("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=createMmlNode("mo",document.createTextNode(symbol.output));node=createMmlNode("mrow",node);node.appendChild(result[0]);return[node,result[1]];}else{node=createMmlNode("mo",document.createTextNode("\u2223"));node=createMmlNode("mrow",node);return[node,str];}
default:str=AMremoveCharsAndBlanks(str,symbol.input.length);return[createMmlNode(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]=createMmlNode("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=createMmlNode((underover?"munderover":"msubsup"),node);node.appendChild(result[0]);node.appendChild(res2[0]);node=createMmlNode("mrow",node);}else{node=createMmlNode((underover?"munder":"msub"),node);node.appendChild(result[0]);}}else{node=createMmlNode(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]=createMmlNode("mo",document.createTextNode("\u25A1"));else AMremoveBrackets(result[0]);str=result[1];AMremoveBrackets(node);node=createMmlNode(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(createMmlNode("mtd",frag));k++;}else frag.appendChild(node.firstChild);}
row.appendChild(createMmlNode("mtd",frag));if(newFrag.childNodes.length>2){newFrag.removeChild(newFrag.firstChild);newFrag.removeChild(newFrag.firstChild);}
table.appendChild(createMmlNode("mtr",row));}
node=createMmlNode("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=createMmlNode("mo",document.createTextNode(symbol.output));newFrag.appendChild(node);}}
return[newFrag,str];}
function parseMath(str,latex){var frag,node;AMnestingDepth=0;frag=latex?LMparseExpr(str.replace(/^\s+/g,""),false,false)[0]:AMparseExpr(str.replace(/^\s+/g,""),false)[0];node=createMmlNode("mstyle",frag);node.setAttribute("mathcolor",mathcolor);node.setAttribute("fontfamily",mathfontfamily);node.setAttribute("mathsize",mathfontsize);if(displaystyle)node.setAttribute("displaystyle","true");node=createMmlNode("math",node);if(showasciiformulaonhover)
node.setAttribute("title",str.replace(/\s+/g," "));return node;}
function strarr2docFrag(arr,linebreaks,latex){var newFrag=document.createDocumentFragment();var expr=false;for(var i=0;i<arr.length;i++){if(expr)newFrag.appendChild(parseMath(arr[i],latex));else{var arri=(linebreaks?arr[i].split("\n\n"):[arr[i]]);newFrag.appendChild(createElementXHTML("span").appendChild(document.createTextNode(arri[0])));for(var j=1;j<arri.length;j++){newFrag.appendChild(createElementXHTML("p"));newFrag.appendChild(createElementXHTML("span").appendChild(document.createTextNode(arri[j])));}}
expr=!expr;}
return newFrag;}
function AMautomathrec(str){var texcommand="\\\\[a-zA-Z]+|\\\\\\s|";var ambigAMtoken="\\b(?:oo|lim|ln|int|oint|del|grad|aleph|prod|prop|sinh|cosh|tanh|cos|sec|pi|tt|fr|sf|sube|supe|sub|sup|det|mod|gcd|lcm|min|max|vec|ddot|ul|chi|eta|nu|mu)(?![a-z])|";var englishAMtoken="\\b(?:sum|ox|log|sin|tan|dim|hat|bar|dot)(?![a-z])|";var secondenglishAMtoken="|\\bI\\b|\\bin\\b|\\btext\\b";var simpleAMtoken="NN|ZZ|QQ|RR|CC|TT|AA|EE|sqrt|dx|dy|dz|dt|xx|vv|uu|nn|bb|cc|csc|cot|alpha|beta|delta|Delta|epsilon|gamma|Gamma|kappa|lambda|Lambda|omega|phi|Phi|Pi|psi|Psi|rho|sigma|Sigma|tau|theta|Theta|xi|Xi|zeta";var letter="[a-zA-HJ-Z](?=(?:[^a-zA-Z]|$|"+ambigAMtoken+englishAMtoken+simpleAMtoken+"))|";var token=letter+texcommand+"\\d+|[-()[\\]{}+=*&^_%\\\@/<>,\\|!:;'~]|\\.(?!(?:\x20|$))|"+ambigAMtoken+englishAMtoken+simpleAMtoken;var re=new RegExp("(^|\\s)((("+token+")\\s?)(("+token+secondenglishAMtoken+")\\s?)+)([,.?]?(?=\\s|$))","g");str=str.replace(re," `$2`$7");var arr=str.split(AMdelimiter1);var re1=new RegExp("(^|\\s)([b-zB-HJ-Z+*<>]|"+texcommand+ambigAMtoken+simpleAMtoken+")(\\s|\\n|$)","g");var re2=new RegExp("(^|\\s)([a-z]|"+texcommand+ambigAMtoken+simpleAMtoken+")([,.])","g");for(i=0;i<arr.length;i++)
if(i%2==0){arr[i]=arr[i].replace(re1," `$2`$3");arr[i]=arr[i].replace(re2," `$2`$3");arr[i]=arr[i].replace(/([{}[\]])/,"`$1`");}
str=arr.join(AMdelimiter1);str=str.replace(/((^|\s)\([a-zA-Z]{2,}.*?)\)`/g,"$1`)");str=str.replace(/`(\((a\s|in\s))(.*?[a-zA-Z]{2,}\))/g,"$1`$3");str=str.replace(/\sin`/g,"` in");str=str.replace(/`(\(\w\)[,.]?(\s|\n|$))/g,"$1`");str=str.replace(/`([0-9.]+|e.g|i.e)`(\.?)/gi,"$1$2");str=str.replace(/`([0-9.]+:)`/g,"$1");return str;}
function processNodeR(n,linebreaks,latex){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"){str=n.nodeValue;if(!(str==null)){str=str.replace(/\r\n\r\n/g,"\n\n");str=str.replace(/\x20+/g," ");str=str.replace(/\s*\r\n/g," ");if(latex){mtch=(str.indexOf("\$")==-1?false:true);str=str.replace(/([^\\])\$/g,"$1 \$");str=str.replace(/^\$/," \$");arr=str.split(" \$");for(i=0;i<arr.length;i++)
arr[i]=arr[i].replace(/\\\$/g,"\$");}else{mtch=false;str=str.replace(new RegExp(AMescape1,"g"),function(){mtch=true;return"AMescape1"});str=str.replace(/\\?end{?a?math}?/i,function(){automathrecognize=false;mtch=true;return""});str=str.replace(/amath\b|\\begin{a?math}/i,function(){automathrecognize=true;mtch=true;return""});arr=str.split(AMdelimiter1);if(automathrecognize)
for(i=0;i<arr.length;i++)
if(i%2==0)arr[i]=AMautomathrec(arr[i]);str=arr.join(AMdelimiter1);arr=str.split(AMdelimiter1);for(i=0;i<arr.length;i++)
arr[i]=arr[i].replace(/AMescape1/g,AMdelimiter1);}
if(arr.length>1||mtch){if(!noMathML){frg=strarr2docFrag(arr,n.nodeType==8,latex);var len=frg.childNodes.length;n.parentNode.replaceChild(frg,n);return len-1;}else return 0;}}}else return 0;}else if(n.nodeName!="math"){for(i=0;i<n.childNodes.length;i++)
i+=processNodeR(n.childNodes[i],linebreaks,latex);}
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")
processNodeR(frag[i],linebreaks,false);}else{try{st=n.innerHTML;}catch(err){}
if(st==null||/amath\b|\\begin{a?math}/i.test(st)||st.indexOf(AMdelimiter1+" ")!=-1||st.slice(-1)==AMdelimiter1||st.indexOf(AMdelimiter1+"<")!=-1||st.indexOf(AMdelimiter1+"\n")!=-1){processNodeR(n,linebreaks,false);}}}
var 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LMnames=[];function LMremoveCharsAndBlanks(str,n){var st;st=str.slice(n);for(var i=0;i<st.length&&st.charCodeAt(i)<=32;i=i+1);return st.slice(i);}
function LMgetSymbol(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=position(LMnames,st,j);if(k<LMnames.length&&str.slice(0,LMnames[k].length)==LMnames[k]){match=LMnames[k];mk=k;i=match.length;}
more=k<LMnames.length&&str.slice(0,LMnames[k].length)>=LMnames[k];}
LMpreviousSymbol=LMcurrentSymbol;if(match!=""){LMcurrentSymbol=LMsymbols[mk].ttype;return LMsymbols[mk];}
LMcurrentSymbol=CONST;k=1;st=str.slice(0,1);if("0"<=st&&st<="9")tagst="mn";else tagst=(("A">st||st>"Z")&&("a">st||st>"z")?"mo":"mi");return{input:st,tag:tagst,output:st,ttype:CONST};}
var LMpreviousSymbol,LMcurrentSymbol;function LMparseSexpr(str){var symbol,node,result,result2,i,st,newFrag=document.createDocumentFragment();str=LMremoveCharsAndBlanks(str,0);symbol=LMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET)
return[null,str,null];if(symbol.ttype==DEFINITION){str=symbol.output+LMremoveCharsAndBlanks(str,symbol.input.length);symbol=LMgetSymbol(str);if(symbol==null||symbol.ttype==RIGHTBRACKET)
return[null,str,null];}
str=LMremoveCharsAndBlanks(str,symbol.input.length);switch(symbol.ttype){case SPACE:node=createMmlNode(symbol.tag);node.setAttribute(symbol.atname,symbol.atval);return[node,str,symbol.tag];case UNDEROVER:if(isIE){if(symbol.input.substr(0,4)=="\\big"){str="\\"+symbol.input.substr(4)+str;symbol=LMgetSymbol(str);symbol.ttype=UNDEROVER;str=LMremoveCharsAndBlanks(str,symbol.input.length);}}
return[createMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];case CONST:var output=symbol.output;if(isIE){if(symbol.input=="'")
output="\u2032";else if(symbol.input=="''")
output="\u2033";else if(symbol.input=="'''")
output="\u2033\u2032";else if(symbol.input=="''''")
output="\u2033\u2033";else if(symbol.input=="\\square")
output="\u25A1";else if(symbol.input.substr(0,5)=="\\frac"){var denom=symbol.input.substr(6,1);if(denom=="5"||denom=="6"){str=symbol.input.replace(/\\frac/,"\\frac ")+str;return[node,str,symbol.tag];}}}
node=createMmlNode(symbol.tag,document.createTextNode(output));return[node,str,symbol.tag];case LONG:node=createMmlNode(symbol.tag,document.createTextNode(symbol.output));node.setAttribute("minsize","1.5");node.setAttribute("maxsize","1.5");node=createMmlNode("mover",node);node.appendChild(createMmlNode("mspace"));return[node,str,symbol.tag];case STRETCHY:if(isIE&&symbol.input=="\\backslash")
symbol.output="\\";node=createMmlNode(symbol.tag,document.createTextNode(symbol.output));if(symbol.input=="|"||symbol.input=="\\vert"||symbol.input=="\\|"||symbol.input=="\\Vert"){node.setAttribute("lspace","0em");node.setAttribute("rspace","0em");}
node.setAttribute("maxsize",symbol.atval);if(symbol.rtag!=null)
return[node,str,symbol.rtag];else
return[node,str,symbol.tag];case BIG:var atval=symbol.atval;if(isIE)
atval=symbol.ieval;symbol=LMgetSymbol(str);if(symbol==null)
return[null,str,null];str=LMremoveCharsAndBlanks(str,symbol.input.length);node=createMmlNode(symbol.tag,document.createTextNode(symbol.output));if(isIE){var space=createMmlNode("mspace");space.setAttribute("height",atval+"ex");node=createMmlNode("mrow",node);node.appendChild(space);}else{node.setAttribute("minsize",atval);node.setAttribute("maxsize",atval);}
return[node,str,symbol.tag];case LEFTBRACKET:if(symbol.input=="\\left"){symbol=LMgetSymbol(str);if(symbol!=null){if(symbol.input==".")
symbol.invisible=true;str=LMremoveCharsAndBlanks(str,symbol.input.length);}}
result=LMparseExpr(str,true,false);if(symbol==null||(typeof symbol.invisible=="boolean"&&symbol.invisible))
node=createMmlNode("mrow",result[0]);else{node=createMmlNode("mo",document.createTextNode(symbol.output));node=createMmlNode("mrow",node);node.appendChild(result[0]);}
return[node,result[1],result[2]];case MATRIX:if(symbol.input=="\\begin{array}"){var mask="";symbol=LMgetSymbol(str);str=LMremoveCharsAndBlanks(str,0);if(symbol==null)
mask="l";else{str=LMremoveCharsAndBlanks(str,symbol.input.length);if(symbol.input!="{")
mask="l";else do{symbol=LMgetSymbol(str);if(symbol!=null){str=LMremoveCharsAndBlanks(str,symbol.input.length);if(symbol.input!="}")
mask=mask+symbol.input;}}while(symbol!=null&&symbol.input!=""&&symbol.input!="}");}
result=LMparseExpr("{"+str,true,true);node=createMmlNode("mtable",result[0]);mask=mask.replace(/l/g,"left ");mask=mask.replace(/r/g,"right ");mask=mask.replace(/c/g,"center ");node.setAttribute("columnalign",mask);node.setAttribute("displaystyle","false");if(isIE)
return[node,result[1],null];var lspace=createMmlNode("mspace");lspace.setAttribute("width","0.167em");var rspace=createMmlNode("mspace");rspace.setAttribute("width","0.167em");var node1=createMmlNode("mrow",lspace);node1.appendChild(node);node1.appendChild(rspace);return[node1,result[1],null];}else{result=LMparseExpr("{"+str,true,true);node=createMmlNode("mtable",result[0]);if(isIE)
node.setAttribute("columnspacing","0.25em");else
node.setAttribute("columnspacing","0.167em");node.setAttribute("columnalign","right center left");node.setAttribute("displaystyle","true");node=createMmlNode("mrow",node);return[node,result[1],null];}
case TEXT:if(str.charAt(0)=="{")i=str.indexOf("}");else i=0;if(i==-1)
i=str.length;st=str.slice(1,i);if(st.charAt(0)==" "){node=createMmlNode("mspace");node.setAttribute("width","0.33em");newFrag.appendChild(node);}
newFrag.appendChild(createMmlNode(symbol.tag,document.createTextNode(st)));if(st.charAt(st.length-1)==" "){node=createMmlNode("mspace");node.setAttribute("width","0.33em");newFrag.appendChild(node);}
str=LMremoveCharsAndBlanks(str,i+1);return[createMmlNode("mrow",newFrag),str,null];case UNARY:result=LMparseSexpr(str);if(result[0]==null)return[createMmlNode(symbol.tag,document.createTextNode(symbol.output)),str];if(typeof symbol.func=="boolean"&&symbol.func){st=str.charAt(0);if(st=="^"||st=="_"||st==","){return[createMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];}else{node=createMmlNode("mrow",createMmlNode(symbol.tag,document.createTextNode(symbol.output)));if(isIE){var space=createMmlNode("mspace");space.setAttribute("width","0.167em");node.appendChild(space);}
node.appendChild(result[0]);return[node,result[1],symbol.tag];}}
if(symbol.input=="\\sqrt"){if(isIE){var space=createMmlNode("mspace");space.setAttribute("height","1.2ex");space.setAttribute("width","0em");node=createMmlNode(symbol.tag,result[0])
node.appendChild(space);return[node,result[1],symbol.tag];}else
return[createMmlNode(symbol.tag,result[0]),result[1],symbol.tag];}else if(typeof symbol.acc=="boolean"&&symbol.acc){node=createMmlNode(symbol.tag,result[0]);var output=symbol.output;if(isIE){if(symbol.input=="\\hat")
output="\u0302";else if(symbol.input=="\\widehat")
output="\u005E";else if(symbol.input=="\\bar")
output="\u00AF";else if(symbol.input=="\\grave")
output="\u0300";else if(symbol.input=="\\tilde")
output="\u0303";}
var node1=createMmlNode("mo",document.createTextNode(output));if(symbol.input=="\\vec"||symbol.input=="\\check")
node1.setAttribute("maxsize","1.2");if(isIE&&symbol.input=="\\bar")
node1.setAttribute("maxsize","0.5");if(symbol.input=="\\underbrace"||symbol.input=="\\underline")
node1.setAttribute("accentunder","true");else
node1.setAttribute("accent","true");node.appendChild(node1);if(symbol.input=="\\overbrace"||symbol.input=="\\underbrace")
node.ttype=UNDEROVER;return[node,result[1],symbol.tag];}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]=createMmlNode("mo").appendChild(document.createTextNode(newst));else result[0].replaceChild(createMmlNode("mo").appendChild(document.createTextNode(newst)),result[0].childNodes[i]);}}
node=createMmlNode(symbol.tag,result[0]);node.setAttribute(symbol.atname,symbol.atval);if(symbol.input=="\\scriptstyle"||symbol.input=="\\scriptscriptstyle")
node.setAttribute("displaystyle","false");return[node,result[1],symbol.tag];}
case BINARY:result=LMparseSexpr(str);if(result[0]==null)return[createMmlNode("mo",document.createTextNode(symbol.input)),str,null];result2=LMparseSexpr(result[1]);if(result2[0]==null)return[createMmlNode("mo",document.createTextNode(symbol.input)),str,null];if(symbol.input=="\\root"||symbol.input=="\\stackrel")
newFrag.appendChild(result2[0]);newFrag.appendChild(result[0]);if(symbol.input=="\\frac")newFrag.appendChild(result2[0]);return[createMmlNode(symbol.tag,newFrag),result2[1],symbol.tag];case INFIX:str=LMremoveCharsAndBlanks(str,symbol.input.length);return[createMmlNode("mo",document.createTextNode(symbol.output)),str,symbol.tag];default:return[createMmlNode(symbol.tag,document.createTextNode(symbol.output)),str,symbol.tag];}}
function LMparseIexpr(str){var symbol,sym1,sym2,node,result,tag,underover;str=LMremoveCharsAndBlanks(str,0);sym1=LMgetSymbol(str);result=LMparseSexpr(str);node=result[0];str=result[1];tag=result[2];symbol=LMgetSymbol(str);if(symbol.ttype==INFIX){str=LMremoveCharsAndBlanks(str,symbol.input.length);result=LMparseSexpr(str);if(result[0]==null)
result[0]=createMmlNode("mo",document.createTextNode("\u25A1"));str=result[1];tag=result[2];if(symbol.input=="_"||symbol.input=="^"){sym2=LMgetSymbol(str);tag=null;underover=((sym1.ttype==UNDEROVER)||(node.ttype==UNDEROVER));if(symbol.input=="_"&&sym2.input=="^"){str=LMremoveCharsAndBlanks(str,sym2.input.length);var res2=LMparseSexpr(str);str=res2[1];tag=res2[2];node=createMmlNode((underover?"munderover":"msubsup"),node);node.appendChild(result[0]);node.appendChild(res2[0]);}else if(symbol.input=="_"){node=createMmlNode((underover?"munder":"msub"),node);node.appendChild(result[0]);}else{node=createMmlNode((underover?"mover":"msup"),node);node.appendChild(result[0]);}
node=createMmlNode("mrow",node);}else{node=createMmlNode(symbol.tag,node);if(symbol.input=="\\atop"||symbol.input=="\\choose")
node.setAttribute("linethickness","0ex");node.appendChild(result[0]);if(symbol.input=="\\choose")
node=createMmlNode("mfenced",node);}}
return[node,str,tag];}
function LMparseExpr(str,rightbracket,matrix){var symbol,node,result,i,tag,newFrag=document.createDocumentFragment();do{str=LMremoveCharsAndBlanks(str,0);result=LMparseIexpr(str);node=result[0];str=result[1];tag=result[2];symbol=LMgetSymbol(str);if(node!=undefined){if((tag=="mn"||tag=="mi")&&symbol!=null&&typeof symbol.func=="boolean"&&symbol.func){var space=createMmlNode("mspace");space.setAttribute("width","0.167em");node=createMmlNode("mrow",node);node.appendChild(space);}
newFrag.appendChild(node);}}while((symbol.ttype!=RIGHTBRACKET)&&symbol!=null&&symbol.output!="");tag=null;if(symbol.ttype==RIGHTBRACKET){if(symbol.input=="\\right"){str=LMremoveCharsAndBlanks(str,symbol.input.length);symbol=LMgetSymbol(str);if(symbol!=null&&symbol.input==".")
symbol.invisible=true;if(symbol!=null)
tag=symbol.rtag;}
if(symbol!=null)
str=LMremoveCharsAndBlanks(str,symbol.input.length);var len=newFrag.childNodes.length;if(matrix&&len>0&&newFrag.childNodes[len-1].nodeName=="mrow"&&len>1&&newFrag.childNodes[len-2].nodeName=="mo"&&newFrag.childNodes[len-2].firstChild.nodeValue=="&"){var pos=[];var m=newFrag.childNodes.length;for(i=0;matrix&&i<m;i=i+2){pos[i]=[];node=newFrag.childNodes[i];for(var j=0;j<node.childNodes.length;j++)
if(node.childNodes[j].firstChild.nodeValue=="&")
pos[i][pos[i].length]=j;}
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;for(j=0;j<n;j++){if(typeof pos[i][k]!="undefined"&&j==pos[i][k]){node.removeChild(node.firstChild);row.appendChild(createMmlNode("mtd",frag));k++;}else frag.appendChild(node.firstChild);}
row.appendChild(createMmlNode("mtd",frag));if(newFrag.childNodes.length>2){newFrag.removeChild(newFrag.firstChild);newFrag.removeChild(newFrag.firstChild);}
table.appendChild(createMmlNode("mtr",row));}
return[table,str];}
if(typeof symbol.invisible!="boolean"||!symbol.invisible){node=createMmlNode("mo",document.createTextNode(symbol.output));newFrag.appendChild(node);}}
return[newFrag,str,tag];}
var tcnt=0,dcnt=0;function simpleLaTeXformatting(st){st=st.replace(/\$\$((.|\n)*?)\$\$/g,"<p align=\"center\">$\\displaystyle{$1}$</p>");st=st.replace(/\\begin{(theorem|lemma|proposition|corollary)}((.|\n)*?)\\end{\1}/g,function(r,s,t){tcnt++;return"<b>"+s.charAt(0).toUpperCase()+s.slice(1)+" "+tcnt+".</b> <i>"+t.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+"</i>"});st=st.replace(/\\begin{(definition|example|remark|problem|exercise|conjecture|solution)}((.|\n)*?)\\end{\1}/g,function(r,s,t){dcnt++;return"<b>"+s.charAt(0).toUpperCase()+s.slice(1)+" "+dcnt+".</b> "+t.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")});st=st.replace(/\\begin{proof}((.|\n)*?)\\end{proof}/g,function(s,t){return"<i>Proof:</i> "+t.replace(/^\s*<\/?\w+\/?>|\s*<\/?\w+\/?>$/g,"")+" &#x25A1;"});st=st.replace(/\\emph{(.*?)}/g,"<em>$1</em>");st=st.replace(/\\textbf{(.*?)}/g,"<b>$1</b>");st=st.replace(/\\cite{(.*?)}/g,"[$1]");st=st.replace(/\\chapter{(.*?)}/g,"<h2>$1</h2>");st=st.replace(/\\section{(.*?)}(\s*<\/?(br|p)\s?\/?>)?/g,"<h3>$1</h3>");st=st.replace(/\\subsection{((.|\n)*?)}/g,"<h4>$1</h4>");st=st.replace(/\\begin{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"<ul>");st=st.replace(/\\item\s((.|\n)*?)(?=(\\item|\\end))/g,"<li>$1</li>");st=st.replace(/\\end{itemize}(\s*<\/?(br|p)\s?\/?>)?/g,"</ul>");st=st.replace(/\\begin{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"<ol>");st=st.replace(/\\end{enumerate}(\s*<\/?(br|p)\s?\/?>)?/g,"</ol>");st=st.replace(/\\item\[(.*?)]{(.*?)}/g,"<dt>$1</dt><dd>$2</dd>");st=st.replace(/\\begin{description}/g,"<dl>");st=st.replace(/\\end{description}/g,"</dl>");st=st.replace(/\\newline\b/g,"<br/>");st=st.replace(/\\newpage\b/g,"<br style=\"page-break-after:always;\">");st=st.replace(/\\par\b/g,"<p>&nbsp;</p>");st=st.replace(/\\bigskip/g,"<p style=\"margin-bottom:0.5in\">&nbsp;</p>");st=st.replace(/\\medskip/g,"<p style=\"margin-bottom:0.3in\">&nbsp;</p>");st=st.replace(/\\smallskip/g,"<p style=\"margin-bottom:0.15in\">&nbsp;</p>");st=st.replace(/\\begin{center}((.|\n)*?)\\end{center}/g,"<center>$1</center>");return st}
function ASCIIandgraphformatting(st){st=st.replace(/<sup>(.*?)<\/sup>(\s|(\S))/gi,"^{$1} $3");st=st.replace(/(Proof:)/g,"<i>$1</i>");st=st.replace(/QED/g,"&nbsp; &nbsp; &#x25A1;");st=st.replace(/(\\?end{?a?math}?)/ig,"<span></span>$1");st=st.replace(/(\bamath\b|\\begin{a?math})/ig,"<span></span>$1");st=st.replace(/([>\n])(Theorem|Lemma|Proposition|Corollary|Definition|Example|Remark|Problem|Exercise|Conjecture|Solution)(:|\W\W?(\w|\s|-|\.)*?\W?:)/g,"$1<b>$2$3</b>");st=st.replace(/<embed\s+class\s?=\s?"?ASCIIsvg"?/gi,"<embed class=\"ASCIIsvg\" src=\""+dsvglocation+"d.svg\" wmode=\"transparent\"");st=st.replace(/(?:\\begin{a?graph}|\bagraph|\(:graph\s)((.|\n)*?)(?:\\end{a?graph}|enda?graph|:\))/g,function(s,t){return"<table><tr><td><div class=\"ASCIIsvg\"><embed class=\"ASCIIsvg\" src=\""+dsvglocation+"d.svg\" wmode=\"transparent\" script=\'"+t.replace(/<\/?(br|p|pre)\s?\/?>/gi,"\n")+"\'/></div></td></tr></table>"});st=st.replace(/insertASCIIMathCalculator/g,"<div class=\"ASCIIMathCalculator\"></div>");return st}
function LMprocessNode(n){var frag,st;try{st=n.innerHTML;}catch(err){}
var am=/amath\b|graph/i.test(st);if((st==null||st.indexOf("\$ ")!=-1||st.indexOf("\$<")!=-1||st.indexOf("\\begin")!=-1||am||st.slice(-1)=="$"||st.indexOf("\$\n")!=-1)&&!/edit-content|HTMLArea|wikiedit|wpTextbox1/.test(st)){if(!avoidinnerHTML&&translateLaTeXformatting)
st=simpleLaTeXformatting(st);if(st!=null&&am&&!avoidinnerHTML){st=ASCIIandgraphformatting(st);}
st=st.replace(/%7E/g,"~");if(!avoidinnerHTML)n.innerHTML=st;processNodeR(n,false,true);}}
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function C(x,k){var res=1;for(var i=0;i<k;i++)res*=(x-i)/(k-i);return res;}
function chop(x,n){if(n==null)n=0;return Math.floor(x*Math.pow(10,n))/Math.pow(10,n);}
function ran(a,b,n){if(n==null)n=0;return chop((b+Math.pow(10,-n)-a)*Math.random()+a,n);}
function myCreateElementSVG(t){if(isIE)return doc.createElement(t);else return doc.createElementNS("http://www.w3.org/2000/svg",t);}
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function showobj(obj){var st="",i;for(i in obj)
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curtop=obj.offsetTop
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function checkSVG(){if(navigator.appName.slice(0,8)=="Netscape")
if(window['SVGElement'])noSVG=null;else noSVG=true;else if(navigator.appName.slice(0,9)=="Microsoft")
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noSVG=null;else noSVG=true;if(noSVG&&notifyIfNoSVG){var msg="To view the ASCIIsvg images use Internet Explorer + Adobe SVGviewer or Mozilla Firefox 2.0 or later."
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function setText(st,id){var node=document.getElementById(id);if(node!=null)
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function getY(evt){var svgroot=evt.target.parentNode;pos=findPos(svgroot.parentNode);return(svgroot.getAttribute("height")-svgroot.getAttribute("oy")-(evt.clientY+(isIE?0:window.pageYOffset)-pos[1]))/parseFloat(svgroot.getAttribute("yunitlength"));}
function translateandeval(src){var errstr;src=src.replace(/plot\(\x20*([^\"f\[][^\n\r;]+?)\,/g,"plot\(\"$1\",");src=src.replace(/plot\(\x20*([^\"f\[][^\n\r;]+)\)/g,"plot(\"$1\")");src=src.replace(/([=[(,]\x20*)\(([-a-z0-9./+*]+?),([-a-z0-9./+*]+?)\)/g,"$1[$2,$3]");src=src.replace(/([0-9])([a-df-zA-Z]|e^)/g,"$1*$2");src=src.replace(/\)([\(0-9a-zA-Z])/g,"\)*$1");try{with(Math)eval(src);}catch(err){if(err!="wait"){if(typeof err=="object")
errstr=err.name+" "+err.message+" "+err.number+" "+err.description;else errstr=err;alert(errstr+"\n"+src)}}}
var lastSlot=0;function drawPictures(){var src,id,dsvg,nd,node,ht,index,cols,arr,i,node2;var ASbody=document.getElementsByTagName("body")[0];pictures=getElementsByClass(ASbody,"embed","ASCIIsvg");var len=pictures.length;if(len==0)return;for(index=lastSlot;index<len+lastSlot;index++){width=null;height=null;xmin=null;xmax=null;ymin=null;ymax=null;xscl=null;xgrid=null;yscl=null;ygrid=null;initialized=false;picture=pictures[index-lastSlot];src=picture.getAttribute("script");if(src==null)src="";if(!/axes\b|initPicture/.test(src)){var i=0;while(/((yscl|ymax|ymin|xscl|xmax|xmin|\bwidth|\bheight)\s*=\s*-?\d*(\d\.|\.\d|\d)\d*\s*;?)/.test(src.slice(i)))i++;src=(i==0?"axes(); "+src:src.slice(0,i)+src.slice(i).replace(/((scl|max|min|idth|eight)\s*=\s*-?\d*(\d\.|\.\d|\d)\d*\s*;?)/,"$1\naxes();"));}
ht=picture.getAttribute("height");if(isIE){picture.setAttribute("wmode","transparent");}
if(document.getElementById("picture"+(index+1)+"mml")==null){picture.parentNode.style.position="relative";node=createElementXHTML("div");node.style.position="absolute";node.style.top="0px";node.style.left="0px";node.setAttribute("id","picture"+(index+1)+"mml");picture.parentNode.insertBefore(node,picture.nextSibling);}
if(ht==null)ht="";if(ht==""||src=="")
if(document.getElementById("picture"+(index+1)+"input")==null){node=createElementXHTML("textarea");arr=src.split("\n");cols=0;for(i=0;i<arr.length;i++)cols=Math.max(cols,arr[i].length);node.setAttribute("rows",Math.min(10,arr.length)+1);node.setAttribute("cols",Math.max(Math.min(60,cols),20)+5);if(isIE)src=src.replace(/([^\r])\n/g,"$1\r");node.appendChild(document.createTextNode(src));if(src.indexOf("showcode()")==-1)node.style.display="none";node.setAttribute("id","picture"+(index+1)+"input");picture.parentNode.insertBefore(node,picture.nextSibling);picture.parentNode.insertBefore(createElementXHTML("br"),node);node2=createElementXHTML("button");node2.setAttribute("id","picture"+(index+1)+"button");if(isIE)node2.onclick=function(){updatePicture(this)};else node2.setAttribute("onclick","updatePicture(this)");node2.appendChild(document.createTextNode("Update"));if(src.indexOf("showcode()")==-1)node2.style.display="none";picture.parentNode.insertBefore(node2,node);picture.parentNode.insertBefore(createElementXHTML("br"),node);}else src=document.getElementById("picture"+(index+1)+"input").value;id=picture.getAttribute("id");dsvg=picture.getAttribute("src");if(id==null||id==""){id="picture"+(index+1);picture.setAttribute("id",id);}
translateandeval(src);}
lastSlot+=len;}
function setdefaults(){strokewidth=defaultstrokewidth;stroke=defaultstroke;strokeopacity=defaultstrokeopacity;strokedasharray=defaultstrokedasharray;fill=defaultfill;fillopacity=defaultfillopacity;fontstyle=defaultfontstyle;fontfamily=defaultfontfamily;fontsize=defaultfontsize;fontweight=defaultfontweight;fontstroke=defaultfontstroke;fontfill=defaultfontfill;marker=defaultmarker;endpoints=defaultendpoints;}
function switchTo(id){if(id==undefined)return;var name=id;if(typeof name!="string")name=id.target.parentNode.getAttribute("name");picture=document.getElementById(name);width=picture.getAttribute("width")-0;height=picture.getAttribute("height")-0;setdefaults();if((picture.nodeName=="EMBED"||picture.nodeName=="embed")&&isIE){svgpicture=picture.getSVGDocument().getElementById("root");doc=picture.getSVGDocument();}else{svgpicture=picture;doc=document;}
xunitlength=parseFloat(svgpicture.getAttribute("xunitlength"));yunitlength=parseFloat(svgpicture.getAttribute("yunitlength"));xmin=parseFloat(svgpicture.getAttribute("xmin"));xmax=parseFloat(svgpicture.getAttribute("xmax"));ymin=parseFloat(svgpicture.getAttribute("ymin"));ymax=parseFloat(svgpicture.getAttribute("ymax"));origin=[svgpicture.getAttribute("ox")-0,svgpicture.getAttribute("oy")-0];}
function updatePicture(obj){var node,src,id,top,left;if(typeof obj=="object")id=obj.id.slice(0,-6);else id=(typeof obj=="string"?obj:"picture"+(obj+1));src=document.getElementById(id+"input").value;xmin=null;xmax=null;ymin=null;ymax=null;xscl=null;xgrid=null;yscl=null;ygrid=null;initialized=false;picture=document.getElementById(id);translateandeval(src)}
function changepicturesize(evt,factor){var obj=evt.target;var name=obj.parentNode.getAttribute("name");var pic=document.getElementById(name);var src=document.getElementById(name+"input").value;if(!/height/.test(src))src="height=0; "+src;if(!/width/.test(src))src="width=0; "+src;src=src.replace(/width\s*=\s*\d+/,"width="+(factor*(pic.getAttribute("width")-0)));src=src.replace(/height\s*=\s*\d+/,"height="+(factor*(pic.getAttribute("height")-0)));document.getElementById(name+"input").value=src;updatePicture(name);}
function zoom(evt,factor){switchTo(evt);var obj=evt.target;var name=obj.parentNode.getAttribute("name");var pic=document.getElementById(name);var src=document.getElementById(name+"input").value;var xlen=(xmax-xmin)/2;var ylen=(ymax-ymin)/2;var xcen=getX(evt),ycen=getY(evt);if(!/ymax/.test(src))src="ymax=0; "+src;if(!/ymin/.test(src))src="ymin=0; "+src;if(!/xmax/.test(src))src="xmax=0; "+src;if(!/xmin/.test(src))src="xmin=0; "+src;src=src.replace(/xmin\s*=\s*[-\d.e]+/,"xmin="+(xcen-factor*xlen));src=src.replace(/xmax\s*=\s*[-\d.e]+/,"xmax="+(xcen+factor*xlen));src=src.replace(/ymin\s*=\s*[-\d.e]+/,"ymin="+(ycen-factor*ylen));src=src.replace(/ymax\s*=\s*[-\d.e]+/,"ymax="+(ycen+factor*ylen));document.getElementById(name+"input").value=src;updatePicture(name);}
var sinceFirstClick=0;var dblClkTimer;function timer(){if(sinceFirstClick<60){sinceFirstClick++;setTimeout("timer()",10);}else{clearTimeout(dblClkTimer);dblClkTimer="";}}
function mClick(evt){if(sinceFirstClick!=0){if(sinceFirstClick<=40){if(evt.shiftKey){if(evt.altKey)changepicturesize(evt,2);else zoom(evt,.5);}else if(evt.altKey)zoom(evt,2);else showHideCode(evt);clearTimeout(dblClkTimer);dblClkTimer="";}else{clearTimeout(dblClkTimer);sinceFirstClick=0;dblClkTimer=setTimeout("timer()",10);}}else{sinceFirstClick=0;dblClkTimer=setTimeout("timer()",10);}}
function showHideCode(evt){var obj=evt.target;var name=obj.parentNode.getAttribute("name");var node=document.getElementById(name+"input");node.style.display=(node.style.display=="none"?"":"none");var node=document.getElementById(name+"button");node.style.display=(node.style.display=="none"?"":"none");}
function showcode(){}
function setBorder(x){border=x}
function initPicture(x_min,x_max,y_min,y_max){if(!initialized){setdefaults();initialized=true;if(x_min!=null)xmin=x_min;if(x_max!=null)xmax=x_max;if(y_min!=null)ymin=y_min;if(y_max!=null)ymax=y_max;if(xmin==null)xmin=defaultxmin;if(xmax==null)xmax=defaultxmax;if(typeof xmin!="number"||typeof xmax!="number"||xmin>=xmax)
alert("Picture requires at least two numbers: xmin < xmax");else if(y_max!=null&&(typeof y_min!="number"||typeof y_max!="number"||y_min>=y_max))
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();}else{var qnode=document.createElementNS("http://www.w3.org/2000/svg","svg");qnode.setAttribute("id",picture.getAttribute("id"));qnode.setAttribute("name",picture.getAttribute("id"));qnode.setAttribute("width",picture.getAttribute("width"));qnode.setAttribute("height",picture.getAttribute("height"));picturepos=findPos(picture);if(picture.parentNode!=null){picture.parentNode.replaceChild(qnode,picture);}else{svgpicture.parentNode.replaceChild(qnode,svgpicture);}
svgpicture=qnode;doc=document;}
var nd=document.getElementById(picture.getAttribute("id")+"mml");if(nd!=null)
while(nd.childNodes.length>0)nd.removeChild(nd.lastChild);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 node=myCreateElementSVG("rect");node.setAttribute("x","0");node.setAttribute("y","0");node.setAttribute("width",width);node.setAttribute("height",height);node.setAttribute("style",backgroundstyle);svgpicture.appendChild(node);svgpicture.setAttribute("onmousemove","displayCoord(evt)");svgpicture.setAttribute("onmouseout","removeCoord(evt)");svgpicture.setAttribute("onclick","mClick(evt)");node=myCreateElementSVG("text");node.appendChild(doc.createTextNode(" "));node.setAttribute("id","coords");svgpicture.appendChild(node);node=myCreateElementSVG("text");node.appendChild(doc.createTextNode(" "));node.setAttribute("id","coords");svgpicture.appendChild(node);border=defaultborder;}}}
function line(p,q,id,endpts){var node;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("path");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("d","M"+(p[0]*xunitlength+origin[0])+","+
(height-p[1]*yunitlength-origin[1])+" "+
(q[0]*xunitlength+origin[0])+","+(height-q[1]*yunitlength-origin[1]));node.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null)
node.setAttribute("stroke-dasharray",strokedasharray);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot"){ASdot(p,markersize,markerstroke,markerfill);if(marker=="arrowdot")arrowhead(p,q);ASdot(q,markersize,markerstroke,markerfill);}else if(marker=="arrow")arrowhead(p,q);if(endpts==null&&endpoints!="")endpts=endpoints;if(endpts!=null){if(endpts.indexOf("<-")!=-1)arrowhead(q,p);if(endpts.indexOf("o-")!=-1)dot(p,"open");if(endpts.indexOf("*-")!=-1)dot(p,"closed");if(endpts.indexOf("->")!=-1)arrowhead(p,q);if(endpts.indexOf("-o")!=-1)dot(q,"open");if(endpts.indexOf("-*")!=-1)dot(q,"closed");}}
function path(plist,id,c,endpts){if(c==null)c="";var node,st,i;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("path");node.setAttribute("id",id);svgpicture.appendChild(node);}
if(typeof plist=="string")st=plist;else{st="M";st+=(plist[0][0]*xunitlength+origin[0])+","+
(height-plist[0][1]*yunitlength-origin[1])+" "+c;for(i=1;i<plist.length;i++)
st+=(plist[i][0]*xunitlength+origin[0])+","+
(height-plist[i][1]*yunitlength-origin[1])+" ";}
node.setAttribute("d",st);node.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null)
node.setAttribute("stroke-dasharray",strokedasharray);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot")
for(i=0;i<plist.length;i++)
if(c!="C"&&c!="T"||i!=1&&i!=2)
ASdot(plist[i],markersize,markerstroke,markerfill);if(endpts==null&&endpoints!="")endpts=endpoints;if(endpts!=null){if(endpts.indexOf("<-")!=-1)arrowhead(plist[1],plist[0]);if(endpts.indexOf("o-")!=-1)dot(plist[0],"open");if(endpts.indexOf("*-")!=-1)dot(plist[0],"closed");if(endpts.indexOf("->")!=-1)arrowhead(plist[plist.length-2],plist[plist.length-1]);if(endpts.indexOf("-o")!=-1)dot(plist[plist.length-1],"open");if(endpts.indexOf("-*")!=-1)dot(plist[plist.length-1],"closed");}}
function curve(plist,id,endpts){path(plist,id,"T",endpts);}
function vector(p,q,id){line(p,q,id,"","->");}
function circle(center,radius,id){var node;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("circle");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("cx",center[0]*xunitlength+origin[0]);node.setAttribute("cy",height-center[1]*yunitlength-origin[1]);node.setAttribute("r",radius*xunitlength);node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);}
function loop(p,d,id){if(d==null)d=[1,0];path([p,[p[0]+d[0],p[1]+d[1]],[p[0]-d[1],p[1]+d[0]],p],id,"C");if(marker=="arrow"||marker=="arrowdot")
arrowhead([p[0]+Math.cos(1.4)*d[0]-Math.sin(1.4)*d[1],p[1]+Math.sin(1.4)*d[0]+Math.cos(1.4)*d[1]],p);}
function arc(start,end,radius,id,largearc){var node,v;if(id!=null)node=doc.getElementById(id);if(largearc==null)largearc=0;if(radius==null){v=[end[0]-start[0],end[1]-start[1]];radius=Math.sqrt(v[0]*v[0]+v[1]*v[1]);}
if(node==null){node=myCreateElementSVG("path");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("d","M"+(start[0]*xunitlength+origin[0])+","+
(height-start[1]*yunitlength-origin[1])+" A"+radius*xunitlength+","+
radius*yunitlength+" 0 "+largearc+",0 "+(end[0]*xunitlength+origin[0])+","+
(height-end[1]*yunitlength-origin[1]));node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);if(marker=="arrow"||marker=="arrowdot"){u=[(end[1]-start[1])/4,(start[0]-end[0])/4];v=[(end[0]-start[0])/2,(end[1]-start[1])/2];v=[start[0]+v[0]+u[0],start[1]+v[1]+u[1]];}else v=[start[0],start[1]];if(marker=="dot"||marker=="arrowdot"){ASdot(start,markersize,markerstroke,markerfill);if(marker=="arrowdot")arrowhead(v,end);ASdot(end,markersize,markerstroke,markerfill);}else if(marker=="arrow")arrowhead(v,end);}
function sector(center,start,end,id){var rx=start[0]-center[0],ry=start[1]-center[1];arc(start,end,Math.sqrt(rx*rx+ry*ry),id+"arc");path([end,center,start],id+"path");}
function ellipse(center,rx,ry,id){var node;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("ellipse");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("cx",center[0]*xunitlength+origin[0]);node.setAttribute("cy",height-center[1]*yunitlength-origin[1]);node.setAttribute("rx",rx*xunitlength);node.setAttribute("ry",ry*yunitlength);node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);}
function triangle(p,q,r,id){path([p,q,r,p],id)}
function rect(p,q,id,rx,ry){var node;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("rect");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("x",p[0]*xunitlength+origin[0]);node.setAttribute("y",height-q[1]*yunitlength-origin[1]);node.setAttribute("width",(q[0]-p[0])*xunitlength);node.setAttribute("height",(q[1]-p[1])*yunitlength);if(rx!=null)node.setAttribute("rx",rx*xunitlength);if(ry!=null)node.setAttribute("ry",ry*yunitlength);node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",fill);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);}
function text(p,st,pos,id,fontsty){var dnode,node,dx=0,dy=fontsize/3,str=st.toString();if(/(`|\$)/.test(str)){dnode=document.getElementById(svgpicture.getAttribute("name")+"mml");if(dnode!=null){if(id!=null)node=document.getElementById(id);if(node==null){node=createElementXHTML("div");node.setAttribute("id",id);node.style.position="absolute";dnode.appendChild(node);}
while(node.childNodes.length>0)node.removeChild(node.lastChild);node.appendChild(document.createTextNode(str));if(/`/.test(str))AMprocessNode(node);else LMprocessNode(node);dx=-node.offsetWidth/2;dy=-node.offsetHeight/2;if(pos!=null){if(/above/.test(pos))dy=-node.offsetHeight;if(/below/.test(pos))dy=0;if(/right/.test(pos))dx=0;if(/left/.test(pos))dx=-node.offsetWidth;}
node.style.left=""+(p[0]*xunitlength+origin[0]+dx)+"px";node.style.top=""+(height-p[1]*yunitlength-origin[1]+dy)+"px";}
return p;}
var textanchor="middle";if(pos!=null){if(/above/.test(pos))dy=-fontsize/2;if(/below/.test(pos))dy=fontsize-0;if(/right/.test(pos)){textanchor="start";dx=fontsize/4;}
if(/left/.test(pos)){textanchor="end";dx=-fontsize/4;}}
if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("text");node.setAttribute("id",id);svgpicture.appendChild(node);node.appendChild(doc.createTextNode(str));}
while(node.childNodes.length>1)node.removeChild(node.lastChild);node.lastChild.nodeValue="\xA0"+str+"\xA0";node.setAttribute("x",p[0]*xunitlength+origin[0]+dx);node.setAttribute("y",height-p[1]*yunitlength-origin[1]+dy);node.setAttribute("font-style",(fontsty!=null?fontsty:(str.search(/^[a-zA-Z]$/)!=-1?"italic":fontstyle)));node.setAttribute("font-family",fontfamily);node.setAttribute("font-size",fontsize);node.setAttribute("font-weight",fontweight);node.setAttribute("text-anchor",textanchor);if(fontstroke!="none")node.setAttribute("stroke",fontstroke);if(fontfill!="none")node.setAttribute("fill",fontfill);return p;}
function mtext(p,st,pos,fontsty,fontsz){var textanchor="middle";var dx=0;var dy=fontsize/3;if(pos!=null){if(pos.slice(0,5)=="above")dy=-fontsize/2;if(pos.slice(0,5)=="below")dy=fontsize-0;if(pos.slice(0,5)=="right"||pos.slice(5,10)=="right"){textanchor="start";dx=fontsize/2;}
if(pos.slice(0,4)=="left"||pos.slice(5,9)=="left"){textanchor="end";dx=-fontsize/2;}}
var node=this;if(this.nodeName=="svg"){node=myCreateElementSVG("text");this.appendChild(node);node.appendChild(doc.createTextNode(st));}
node.lastChild.nodeValue=st;node.setAttribute("x",p[0]+dx);node.setAttribute("y",p[1]+dy);node.setAttribute("font-style",(fontsty!=null?fontsty:fontstyle));node.setAttribute("font-family",fontfamily);node.setAttribute("font-size",(fontsz!=null?fontsz:fontsize));node.setAttribute("font-weight",fontweight);node.setAttribute("text-anchor",textanchor);if(fontstroke!="none")node.setAttribute("stroke",fontstroke);if(fontfill!="none")node.setAttribute("fill",fontfill);}
function image(imgurl,p,w,h,id){var node;if(id!=null)node=doc.getElementById(id);if(node==null){node=myCreateElementSVG("image");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("x",p[0]*xunitlength+origin[0]);node.setAttribute("y",height-p[1]*yunitlength-origin[1]);node.setAttribute("width",w);node.setAttribute("height",h);node.setAttribute("xlink:href",imgurl);}
function ASdot(center,radius,s,f){if(s==null)s=stroke;if(f==null)f=fill;var node=myCreateElementSVG("circle");node.setAttribute("cx",center[0]*xunitlength+origin[0]);node.setAttribute("cy",height-center[1]*yunitlength-origin[1]);node.setAttribute("r",radius);node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",s);node.setAttribute("fill",f);svgpicture.appendChild(node);}
function dot(center,typ,label,pos,id){var node;var cx=center[0]*xunitlength+origin[0];var cy=height-center[1]*yunitlength-origin[1];if(id!=null)node=doc.getElementById(id);if(typ=="+"||typ=="-"||typ=="|"){if(node==null){node=myCreateElementSVG("path");node.setAttribute("id",id);svgpicture.appendChild(node);}
if(typ=="+"){node.setAttribute("d"," M "+(cx-ticklength)+" "+cy+" L "+(cx+ticklength)+" "+cy+" M "+cx+" "+(cy-ticklength)+" L "+cx+" "+(cy+ticklength));node.setAttribute("stroke-width",.5);node.setAttribute("stroke",axesstroke);}else{if(typ=="-")node.setAttribute("d"," M "+(cx-ticklength)+" "+cy+" L "+(cx+ticklength)+" "+cy);else node.setAttribute("d"," M "+cx+" "+(cy-ticklength)+" L "+cx+" "+(cy+ticklength));node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);}}else{if(node==null){node=myCreateElementSVG("circle");node.setAttribute("id",id);svgpicture.appendChild(node);}
node.setAttribute("cx",cx);node.setAttribute("cy",cy);node.setAttribute("r",dotradius);node.setAttribute("stroke-width",strokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",(typ=="open"?"white":(typ=="closed"?stroke:markerfill)));}
if(label!=null)
text(center,label,(pos==null?"below":pos),(id==null?id:id+"label"))}
point=dot;function arrowhead(p,q){var up;var v=[p[0]*xunitlength+origin[0],height-p[1]*yunitlength-origin[1]];var w=[q[0]*xunitlength+origin[0],height-q[1]*yunitlength-origin[1]];var u=[w[0]-v[0],w[1]-v[1]];var d=Math.sqrt(u[0]*u[0]+u[1]*u[1]);if(d>0.00000001){u=[u[0]/d,u[1]/d];up=[-u[1],u[0]];var node=myCreateElementSVG("path");node.setAttribute("d","M "+(w[0]-15*u[0]-4*up[0])+" "+
(w[1]-15*u[1]-4*up[1])+" L "+(w[0]-3*u[0])+" "+(w[1]-3*u[1])+" L "+
(w[0]-15*u[0]+4*up[0])+" "+(w[1]-15*u[1]+4*up[1])+" z");node.setAttribute("stroke-width",markerstrokewidth);node.setAttribute("stroke",stroke);node.setAttribute("fill",stroke);node.setAttribute("stroke-opacity",strokeopacity);node.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(node);}}
function chopZ(st){var k=st.indexOf(".");if(k==-1)return st;for(var i=st.length-1;i>k&&st.charAt(i)=="0";i--);if(i==k)i--;return st.slice(0,i+1);}
function grid(dx,dy){axes(dx,dy,null,dx,dy)}
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];x<width;x=x+gdx)
st+=" M"+x+",0"+" "+x+","+height;for(x=origin[0]-gdx;x>0;x=x-gdx)
st+=" M"+x+",0"+" "+x+","+height;for(y=height-origin[1];y<height;y=y+gdy)
st+=" M0,"+y+" "+width+","+y;for(y=height-origin[1]-gdy;y>0;y=y-gdy)
st+=" M0,"+y+" "+width+","+y;pnode.setAttribute("d",st);pnode.setAttribute("stroke-width",.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;x<width;x=x+dx)
st+=" M"+x+","+(height-origin[1]+ticklength)+" "+x+","+
(height-origin[1]-ticklength);for(x=origin[0]-dx;x>0;x=x-dx)
st+=" M"+x+","+(height-origin[1]+ticklength)+" "+x+","+
(height-origin[1]-ticklength);for(y=height-origin[1]+dy;y<height;y=y+dy)
st+=" M"+(origin[0]+ticklength)+","+y+" "+(origin[0]-ticklength)+","+y;for(y=height-origin[1]-dy;y>0;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",.5);pnode.setAttribute("stroke",axesstroke);pnode.setAttribute("fill",fill);pnode.setAttribute("stroke-opacity",strokeopacity);pnode.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(pnode);}
function mathjs(st){st=st.replace(/\s/g,"");if(st.indexOf("^-1")!=-1){st=st.replace(/sin\^-1/g,"arcsin");st=st.replace(/cos\^-1/g,"arccos");st=st.replace(/tan\^-1/g,"arctan");st=st.replace(/sec\^-1/g,"arcsec");st=st.replace(/csc\^-1/g,"arccsc");st=st.replace(/cot\^-1/g,"arccot");st=st.replace(/sinh\^-1/g,"arcsinh");st=st.replace(/cosh\^-1/g,"arccosh");st=st.replace(/tanh\^-1/g,"arctanh");st=st.replace(/sech\^-1/g,"arcsech");st=st.replace(/csch\^-1/g,"arccsch");st=st.replace(/coth\^-1/g,"arccoth");}
st=st.replace(/^e$/g,"(Math.E)");st=st.replace(/^e([^a-zA-Z])/g,"(Math.E)$1");st=st.replace(/([^a-zA-Z])e/g,"$1(Math.E)");st=st.replace(/([0-9])([\(a-zA-Z])/g,"$1*$2");st=st.replace(/\)([\(0-9a-zA-Z])/g,"\)*$1");var i,j,k,ch,nested;while((i=st.indexOf("^"))!=-1){if(i==0)return"Error: missing argument";j=i-1;ch=st.charAt(j);if(ch>="0"&&ch<="9"){j--;while(j>=0&&(ch=st.charAt(j))>="0"&&ch<="9")j--;if(ch=="."){j--;while(j>=0&&(ch=st.charAt(j))>="0"&&ch<="9")j--;}}else if(ch==")"){nested=1;j--;while(j>=0&&nested>0){ch=st.charAt(j);if(ch=="(")nested--;else if(ch==")")nested++;j--;}
while(j>=0&&(ch=st.charAt(j))>="a"&&ch<="z"||ch>="A"&&ch<="Z")
j--;}else if(ch>="a"&&ch<="z"||ch>="A"&&ch<="Z"){j--;while(j>=0&&(ch=st.charAt(j))>="a"&&ch<="z"||ch>="A"&&ch<="Z")
j--;}else{return"Error: incorrect syntax in "+st+" at position "+j;}
if(i==st.length-1)return"Error: missing argument";k=i+1;ch=st.charAt(k);if(ch>="0"&&ch<="9"||ch=="-"){k++;while(k<st.length&&(ch=st.charAt(k))>="0"&&ch<="9")k++;if(ch=="."){k++;while(k<st.length&&(ch=st.charAt(k))>="0"&&ch<="9")k++;}}else if(ch=="("){nested=1;k++;while(k<st.length&&nested>0){ch=st.charAt(k);if(ch=="(")nested++;else if(ch==")")nested--;k++;}}else if(ch>="a"&&ch<="z"||ch>="A"&&ch<="Z"){k++;while(k<st.length&&(ch=st.charAt(k))>="a"&&ch<="z"||ch>="A"&&ch<="Z")k++;}else{return"Error: incorrect syntax in "+st+" at position "+k;}
st=st.slice(0,j+1)+"Math.pow("+st.slice(j+1,i)+","+st.slice(i+1,k)+")"+
st.slice(k);}
while((i=st.indexOf("!"))!=-1){if(i==0)return"Error: missing argument";j=i-1;ch=st.charAt(j);if(ch>="0"&&ch<="9"){j--;while(j>=0&&(ch=st.charAt(j))>="0"&&ch<="9")j--;if(ch=="."){j--;while(j>=0&&(ch=st.charAt(j))>="0"&&ch<="9")j--;}}else if(ch==")"){nested=1;j--;while(j>=0&&nested>0){ch=st.charAt(j);if(ch=="(")nested--;else if(ch==")")nested++;j--;}
while(j>=0&&(ch=st.charAt(j))>="a"&&ch<="z"||ch>="A"&&ch<="Z")
j--;}else if(ch>="a"&&ch<="z"||ch>="A"&&ch<="Z"){j--;while(j>=0&&(ch=st.charAt(j))>="a"&&ch<="z"||ch>="A"&&ch<="Z")
j--;}else{return"Error: incorrect syntax in "+st+" at position "+j;}
st=st.slice(0,j+1)+"factorial("+st.slice(j+1,i)+")"+st.slice(i+1);}
return st;}
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 pth;}
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(obj){var result="";for(var i=0;i<obj.childNodes.length;i++)
result+=obj.childNodes.item(i)+"\n";return result;}
function displayCoord(evt){if(showcoordinates){var svgroot=evt.target.parentNode;var nl=svgroot.childNodes;for(var i=0;i<nl.length&&nl.item(i).nodeName!="text";i++);var cnode=nl.item(i);cnode.mtext=mtext;cnode.mtext([svgroot.getAttribute("width")-(-7),svgroot.getAttribute("height")-7],"("+getX(evt).toFixed(2)+", "+getY(evt).toFixed(2)+")","left","","11");}}
function removeCoord(evt){var svgroot=evt.target.parentNode;var nl=svgroot.childNodes;for(var i=0;i<nl.length&&nl.item(i).nodeName!="text";i++);var cnode=nl.item(i);cnode.mtext=mtext;cnode.mtext([svgroot.getAttribute("width")-0,svgroot.getAttribute("height")-0],"","aboveleft","");}
function initASCIIMathCalculators(li){var i;for(i=0;i<li.length;i++){li[i].innerHTML=calcstr;AMprocessNode(li[i]);}
li=document.getElementsByTagName("textarea");var st;for(i=0;i<li.length;i++){st=li[i].getAttribute("onkeyup");if(st!=null)eval(String(st).replace(/function anonymous\(\)/,""));}}
function calculate(inputId,outputId){var str=document.getElementById(inputId).value;var err="";var ind=str.lastIndexOf("\n");if(ind==str.length-1)str=str.slice(0,ind);str=str.slice(str.lastIndexOf("\n")+1);try{var res=eval(mathjs(str));}catch(e){err="syntax incomplete";}
if(!isNaN(res)&&res!="Infinity")
str="`"+str+" =` "+(Math.abs(res-Math.round(res*1000000)/1000000)<1e-15?Math.round(res*1000000)/1000000:res)+err;else if(str!="")str="`"+str+"` = undefined";var outnode=document.getElementById(outputId);var n=outnode.childNodes.length;for(var i=0;i<n;i++)
outnode.removeChild(outnode.firstChild);outnode.appendChild(document.createTextNode(str));AMprocessNode(outnode);}
function append(st){document.getElementById('in').value+=st;calculate('in','out');document.getElementById('in').scrollTop=1000;document.getElementById('in').focus();}
function clearTextArea(){document.getElementById('in').value="";calculate('in','out');document.getElementById('in').focus();}
var calcstr="<table align=\"center\">\n<tr><th>\nASCIIMath Scientific Calculator\n</th></tr>\n<tr><td>\nClick in the box to use your keyboard or use the buttons\n</td></tr>\n<tr><td>\n<textarea id=\"in\" rows=\"3\" cols=\"40\" onkeyup=\"calculate('in','out')\"></textarea></td></tr>\n<tr><td height=\"50\">Result: &nbsp; &nbsp; <span id=\"out\"></span></td></tr>\n</table>\n<table align=\"center\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody align=\"center\">\n<tr>\n<td colspan=\"4\">\n<button onclick=\"append('sin^-1(')\"><font size=2>`sin^-1`</font></button><button onclick=\"append('cos^-1(')\"><font size=2>`cos^-1`</font></button><button onclick=\"append('tan^-1(')\"><font size=2>`tan^-1`</font></button></td>\n<td><button onclick=\"clearTextArea()\">&nbsp;`C`&nbsp;</button></td>\n\n</tr>\n<tr>\n<td><button onclick=\"append('pi')\">&nbsp;`pi` &nbsp;</button></td>\n<td><button onclick=\"append('sin(')\">&nbsp;`sin`</button></td>\n<td><button onclick=\"append('cos(')\">&nbsp;`cos`</button></td>\n<td><button onclick=\"append('tan(')\">&nbsp;`tan`</button></td>\n<td><button onclick=\"append('^')\">`x^y`</button></td>\n</tr>\n<tr>\n<td><button onclick=\"append('!')\">&nbsp; `!` &nbsp;</button></td>\n\n<td><button onclick=\"append('(')\"><font size=2>&nbsp;&nbsp;`(`&nbsp;&nbsp;</font></button></td>\n<td><button onclick=\"append(')')\"><font size=2>&nbsp;&nbsp;`)`&nbsp;&nbsp;</font></button></td>\n<td><button onclick=\"append('sqrt(')\"><font size=2>`sqrt({::}^\ )`</font></button></td>\n<td><button onclick=\"append('/')\">&nbsp;`-:\ `</button></td>\n</tr>\n<tr>\n<td><button onclick=\"append('log(')\">`log`</button></td>\n<td><button onclick=\"append('7')\">&nbsp; `7` &nbsp;</button></td>\n<td><button onclick=\"append('8')\">&nbsp; `8` &nbsp;</button></td>\n\n<td><button onclick=\"append('9')\">&nbsp; `9` &nbsp;</button></td>\n<td><button onclick=\"append('*')\">&nbsp;`times`&nbsp;</button></td>\n</tr>\n<tr>\n<td><button onclick=\"append('ln(')\">&nbsp;`ln`&nbsp;</button></td>\n<td><button onclick=\"append('4')\">&nbsp; `4` &nbsp;</button></td>\n<td><button onclick=\"append('5')\">&nbsp; `5` &nbsp;</button></td>\n<td><button onclick=\"append('6')\">&nbsp; `6` &nbsp;</button></td>\n\n<td><button onclick=\"append('-')\">&nbsp;`-{::}`&nbsp;</button></td>\n</tr>\n<tr>\n<td><button onclick=\"append('e')\">&nbsp; `e` &nbsp;</button></td>\n<td><button onclick=\"append('1')\">&nbsp;&nbsp;`1` &nbsp;</button></td>\n<td><button onclick=\"append('2')\">&nbsp; `2` &nbsp;</button></td>\n<td><button onclick=\"append('3')\">&nbsp; `3` &nbsp;</button></td>\n<td><button onclick=\"append('+')\">&nbsp;`+{::}`&nbsp;</button></td>\n\n</tr>\n<tr>\n<td> <!--button onclick=\"append('pi')\">&nbsp;`pi` &nbsp;</button--></td>\n<td><button onclick=\"append('0')\">&nbsp; `0` &nbsp;</button></td>\n<td><button onclick=\"append('.')\">&nbsp; `.` &nbsp;</button></td>\n<td><button onclick=\"append('\\n')\">&nbsp;`\"ent\"`</button></td>\n</tr>\n</tbody>\n</table>";function generic()
{if(!init())return;if(translateOnLoad){var nd=document.getElementById("processasciimathinmoodle");if(nd!=null)dsvglocation=nd.className;if(nd!=null||!checkforprocessasciimathinmoodle){translate();if(!noSVG&&translateASCIIsvg)drawPictures();}
var li=getElementsByClass(document,"div","ASCIIMathCalculator");if(!noMathML&&li.length>0)initASCIIMathCalculators(li);}};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;}}