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a;if(b.charAt(0)=="{"&&b.charAt(b.length-1)=="}"){a=b.charAt(1);if(a=="("||a=="["){b="{"+b.substr(2)}a=b.substr(1,6);if(a=="\\left("||a=="\\left["||a=="\\left{"){b="{"+b.substr(7)}a=b.substr(1,12);if(a=="\\left\\lbrace"||a=="\\left\\langle"){b="{"+b.substr(13)}a=b.charAt(b.length-2);if(a==")"||a=="]"){b=b.substr(0,b.length-8)+"}"}a=b.substr(b.length-8,7);if(a=="\\rbrace"||a=="\\rangle"){b=b.substr(0,b.length-14)+"}"}}return b}var AMnestingDepth,AMpreviousSymbol,AMcurrentSymbol;function AMTgetTeXsymbol(a){if(typeof a.val=="boolean"&&a.val){pre=""}else{pre="\\"}if(a.tex==null){return(pre+a.input)}else{return(pre+a.tex)}}function AMTgetTeXbracket(a){if(a.tex==null){return(a.input)}else{return("\\"+a.tex)}}function AMTparseSexpr(h){var c,b,k,d,j,g="";h=AMremoveCharsAndBlanks(h,0);c=AMgetSymbol(h);if(c==null||c.ttype==RIGHTBRACKET&&AMnestingDepth>0){return[null,h]}if(c.ttype==DEFINITION){h=c.output+AMremoveCharsAndBlanks(h,c.input.length);c=AMgetSymbol(h)}switch(c.ttype){case UNDEROVER:case 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c.invisible=="boolean"&&c.invisible){b=createMmlNode("mrow",m[0])}else{b=createMmlNode("mo",document.createTextNode(c.output));b=createMmlNode("mrow",b);b.appendChild(m[0])}return[b,m[1]];case TEXT:if(c!=AMquote){h=AMremoveCharsAndBlanks(h,c.input.length)}if(h.charAt(0)=="{"){f=h.indexOf("}")}else{if(h.charAt(0)=="("){f=h.indexOf(")")}else{if(h.charAt(0)=="["){f=h.indexOf("]")}else{if(c==AMquote){f=h.slice(1).indexOf('"')+1}else{f=0}}}}if(f==-1){f=h.length}l=h.slice(1,f);if(l.charAt(0)==" "){b=createMmlNode("mspace");b.setAttribute("width","1ex");g.appendChild(b)}g.appendChild(createMmlNode(c.tag,document.createTextNode(l)));if(l.charAt(l.length-1)==" "){b=createMmlNode("mspace");b.setAttribute("width","1ex");g.appendChild(b)}h=AMremoveCharsAndBlanks(h,f+1);return[createMmlNode("mrow",g),h];case UNARY:h=AMremoveCharsAndBlanks(h,c.input.length);m=AMparseSexpr(h);if(m[0]==null){return[createMmlNode(c.tag,document.createTextNode(c.output)),h]}if(typeof c.func=="boolean"&&c.func){l=h.charAt(0);if(l=="^"||l=="_"||l=="/"||l=="|"||l==","){return[createMmlNode(c.tag,document.createTextNode(c.output)),h]}else{b=createMmlNode("mrow",createMmlNode(c.tag,document.createTextNode(c.output)));b.appendChild(m[0]);return[b,m[1]]}}AMremoveBrackets(m[0]);if(c.input=="sqrt"){return[createMmlNode(c.tag,m[0]),m[1]]}else{if(typeof c.acc=="boolean"&&c.acc){b=createMmlNode(c.tag,m[0]);b.appendChild(createMmlNode("mo",document.createTextNode(c.output)));return[b,m[1]]}else{if(!isIE&&typeof c.codes!="undefined"){for(f=0;f<m[0].childNodes.length;f++){if(m[0].childNodes[f].nodeName=="mi"||m[0].nodeName=="mi"){l=(m[0].nodeName=="mi"?m[0].firstChild.nodeValue:m[0].childNodes[f].firstChild.nodeValue);var k=[];for(var 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SPACE:h=AMremoveCharsAndBlanks(h,c.input.length);b=createMmlNode("mspace");b.setAttribute("width","1ex");g.appendChild(b);g.appendChild(createMmlNode(c.tag,document.createTextNode(c.output)));b=createMmlNode("mspace");b.setAttribute("width","1ex");g.appendChild(b);return[createMmlNode("mrow",g),h];case LEFTRIGHT:AMnestingDepth++;h=AMremoveCharsAndBlanks(h,c.input.length);m=AMparseExpr(h,false);AMnestingDepth--;var l="";if(m[0].lastChild!=null){l=m[0].lastChild.firstChild.nodeValue}if(l=="|"){b=createMmlNode("mo",document.createTextNode(c.output));b=createMmlNode("mrow",b);b.appendChild(m[0]);return[b,m[1]]}else{b=createMmlNode("mo",document.createTextNode("\u2223"));b=createMmlNode("mrow",b);return[b,h]}default:h=AMremoveCharsAndBlanks(h,c.input.length);return[createMmlNode(c.tag,document.createTextNode(c.output)),h]}}function AMparseIexpr(h){var 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s,p,f,w,A=[],g=document.createDocumentFragment();do{o=AMremoveCharsAndBlanks(o,0);f=AMparseIexpr(o);p=f[0];o=f[1];s=AMgetSymbol(o);if(s.ttype==INFIX&&s.input=="/"){o=AMremoveCharsAndBlanks(o,s.input.length);f=AMparseIexpr(o);if(f[0]==null){f[0]=createMmlNode("mo",document.createTextNode("\u25A1"))}else{AMremoveBrackets(f[0])}o=f[1];AMremoveBrackets(p);p=createMmlNode(s.tag,p);p.appendChild(f[0]);g.appendChild(p);s=AMgetSymbol(o)}else{if(p!=undefined){g.appendChild(p)}}}while((s.ttype!=RIGHTBRACKET&&(s.ttype!=LEFTRIGHT||l)||AMnestingDepth==0)&&s!=null&&s.output!="");if(s.ttype==RIGHTBRACKET||s.ttype==LEFTRIGHT){var x=g.childNodes.length;if(x>0&&g.childNodes[x-1].nodeName=="mrow"&&x>1&&g.childNodes[x-2].nodeName=="mo"&&g.childNodes[x-2].firstChild.nodeValue==","){var z=g.childNodes[x-1].lastChild.firstChild.nodeValue;if(z==")"||z=="]"){var b=g.childNodes[x-1].firstChild.firstChild.nodeValue;if(b=="("&&z==")"&&s.output!="}"||b=="["&&z=="]"){var c=[];var t=true;var q=g.childNodes.length;for(w=0;t&&w<q;w=w+2){c[w]=[];p=g.childNodes[w];if(t){t=p.nodeName=="mrow"&&(w==q-1||p.nextSibling.nodeName=="mo"&&p.nextSibling.firstChild.nodeValue==",")&&p.firstChild.firstChild.nodeValue==b&&p.lastChild.firstChild.nodeValue==z}if(t){for(var v=0;v<p.childNodes.length;v++){if(p.childNodes[v].firstChild.nodeValue==","){c[w][c[w].length]=v}}}if(t&&w>1){t=c[w].length==c[w-2].length}}if(t){var d,a,h,r,y=document.createDocumentFragment();for(w=0;w<q;w=w+2){d=document.createDocumentFragment();a=document.createDocumentFragment();p=g.firstChild;h=p.childNodes.length;r=0;p.removeChild(p.firstChild);for(v=1;v<h-1;v++){if(typeof c[w][r]!="undefined"&&v==c[w][r]){p.removeChild(p.firstChild);d.appendChild(createMmlNode("mtd",a));r++}else{a.appendChild(p.firstChild)}}d.appendChild(createMmlNode("mtd",a));if(g.childNodes.length>2){g.removeChild(g.firstChild);g.removeChild(g.firstChild)}y.appendChild(createMmlNode("mtr",d))}p=createMmlNode("mtable",y);if(typeof 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d=="string"?d:"picture"+(d+1))}f=document.getElementById(g+"input").value;xmin=null;xmax=null;ymin=null;ymax=null;xscl=null;xgrid=null;yscl=null;ygrid=null;initialized=false;picture=document.getElementById(g);translateandeval(f)}function changepicturesize(a,d){var f=a.target;var c=f.parentNode.getAttribute("name");var b=document.getElementById(c);var g=document.getElementById(c+"input").value;if(!/height/.test(g)){g="height=0; "+g}if(!/width/.test(g)){g="width=0; "+g}g=g.replace(/width\s*=\s*\d+/,"width="+(d*(b.getAttribute("width")-0)));g=g.replace(/height\s*=\s*\d+/,"height="+(d*(b.getAttribute("height")-0)));document.getElementById(c+"input").value=g;updatePicture(c)}function zoom(k,j){switchTo(k);var g=k.target;var c=g.parentNode.getAttribute("name");var h=document.getElementById(c);var b=document.getElementById(c+"input").value;var d=(xmax-xmin)/2;var l=(ymax-ymin)/2;var f=getX(k),a=getY(k);if(!/ymax/.test(b)){b="ymax=0; "+b}if(!/ymin/.test(b)){b="ymin=0; "+b}if(!/xmax/.test(b)){b="xmax=0; "+b}if(!/xmin/.test(b)){b="xmin=0; "+b}b=b.replace(/xmin\s*=\s*[-\d.e]+/,"xmin="+(f-j*d));b=b.replace(/xmax\s*=\s*[-\d.e]+/,"xmax="+(f+j*d));b=b.replace(/ymin\s*=\s*[-\d.e]+/,"ymin="+(a-j*l));b=b.replace(/ymax\s*=\s*[-\d.e]+/,"ymax="+(a+j*l));document.getElementById(c+"input").value=b;updatePicture(c)}var sinceFirstClick=0;var dblClkTimer;function timer(){if(sinceFirstClick<60){sinceFirstClick++;setTimeout("timer()",10)}else{clearTimeout(dblClkTimer);dblClkTimer=""}}function mClick(a){if(sinceFirstClick!=0){if(sinceFirstClick<=40){if(a.shiftKey){if(a.altKey){changepicturesize(a,2)}else{zoom(a,0.5)}}else{if(a.altKey){zoom(a,2)}else{showHideCode(a)}}clearTimeout(dblClkTimer);dblClkTimer=""}else{clearTimeout(dblClkTimer);sinceFirstClick=0;dblClkTimer=setTimeout("timer()",10)}}else{sinceFirstClick=0;dblClkTimer=setTimeout("timer()",10)}}function showHideCode(a){var d=a.target;var b=d.parentNode.getAttribute("name");var c=document.getElementById(b+"input");c.style.display=(c.style.display=="none"?"":"none");var c=document.getElementById(b+"button");c.style.display=(c.style.display=="none"?"":"none")}function showcode(){}function setBorder(a){border=a}function initPicture(h,f,c,a){if(!initialized){setdefaults();initialized=true;if(h!=null){xmin=h}if(f!=null){xmax=f}if(c!=null){ymin=c}if(a!=null){ymax=a}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(a!=null&&(typeof c!="number"||typeof a!="number"||c>=a)){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 b=document.createElementNS("http://www.w3.org/2000/svg","svg");b.setAttribute("id",picture.getAttribute("id"));b.setAttribute("name",picture.getAttribute("id"));b.setAttribute("width",picture.getAttribute("width"));b.setAttribute("height",picture.getAttribute("height"));picturepos=findPos(picture);if(picture.parentNode!=null){picture.parentNode.replaceChild(b,picture)}else{svgpicture.parentNode.replaceChild(b,svgpicture)}svgpicture=b;doc=document}var g=document.getElementById(picture.getAttribute("id")+"mml");if(g!=null){while(g.childNodes.length>0){g.removeChild(g.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 d=myCreateElementSVG("rect");d.setAttribute("x","0");d.setAttribute("y","0");d.setAttribute("width",width);d.setAttribute("height",height);d.setAttribute("style",backgroundstyle);svgpicture.appendChild(d);svgpicture.setAttribute("onmousemove","displayCoord(evt)");svgpicture.setAttribute("onmouseout","removeCoord(evt)");svgpicture.setAttribute("onclick","mClick(evt)");d=myCreateElementSVG("text");d.appendChild(doc.createTextNode(" "));d.setAttribute("id","coords");svgpicture.appendChild(d);d=myCreateElementSVG("text");d.appendChild(doc.createTextNode(" "));d.setAttribute("id","coords");svgpicture.appendChild(d);border=defaultborder}}}}function line(d,c,f,b){var a;if(f!=null){a=doc.getElementById(f)}if(a==null){a=myCreateElementSVG("path");a.setAttribute("id",f);svgpicture.appendChild(a)}a.setAttribute("d","M"+(d[0]*xunitlength+origin[0])+","+(height-d[1]*yunitlength-origin[1])+" "+(c[0]*xunitlength+origin[0])+","+(height-c[1]*yunitlength-origin[1]));a.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null){a.setAttribute("stroke-dasharray",strokedasharray)}a.setAttribute("stroke",stroke);a.setAttribute("fill",fill);a.setAttribute("stroke-opacity",strokeopacity);a.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot"){ASdot(d,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(d,c)}ASdot(c,markersize,markerstroke,markerfill)}else{if(marker=="arrow"){arrowhead(d,c)}}if(b==null&&endpoints!=""){b=endpoints}if(b!=null){if(b.indexOf("<-")!=-1){arrowhead(c,d)}if(b.indexOf("o-")!=-1){dot(d,"open")}if(b.indexOf("*-")!=-1){dot(d,"closed")}if(b.indexOf("->")!=-1){arrowhead(d,c)}if(b.indexOf("-o")!=-1){dot(c,"open")}if(b.indexOf("-*")!=-1){dot(c,"closed")}}}function path(g,j,h,f){if(h==null){h=""}var d,a,b;if(j!=null){d=doc.getElementById(j)}if(d==null){d=myCreateElementSVG("path");d.setAttribute("id",j);svgpicture.appendChild(d)}if(typeof g=="string"){a=g}else{a="M";a+=(g[0][0]*xunitlength+origin[0])+","+(height-g[0][1]*yunitlength-origin[1])+" "+h;for(b=1;b<g.length;b++){a+=(g[b][0]*xunitlength+origin[0])+","+(height-g[b][1]*yunitlength-origin[1])+" "}}d.setAttribute("d",a);d.setAttribute("stroke-width",strokewidth);if(strokedasharray!=null){d.setAttribute("stroke-dasharray",strokedasharray)}d.setAttribute("stroke",stroke);d.setAttribute("fill",fill);d.setAttribute("stroke-opacity",strokeopacity);d.setAttribute("fill-opacity",fillopacity);if(marker=="dot"||marker=="arrowdot"){for(b=0;b<g.length;b++){if(h!="C"&&h!="T"||b!=1&&b!=2){ASdot(g[b],markersize,markerstroke,markerfill)}}}if(f==null&&endpoints!=""){f=endpoints}if(f!=null){if(f.indexOf("<-")!=-1){arrowhead(g[1],g[0])}if(f.indexOf("o-")!=-1){dot(g[0],"open")}if(f.indexOf("*-")!=-1){dot(g[0],"closed")}if(f.indexOf("->")!=-1){arrowhead(g[g.length-2],g[g.length-1])}if(f.indexOf("-o")!=-1){dot(g[g.length-1],"open")}if(f.indexOf("-*")!=-1){dot(g[g.length-1],"closed")}}}function curve(b,c,a){path(b,c,"T",a)}function vector(b,a,c){line(b,a,c,"","->")}function circle(b,a,d){var c;if(d!=null){c=doc.getElementById(d)}if(c==null){c=myCreateElementSVG("circle");c.setAttribute("id",d);svgpicture.appendChild(c)}c.setAttribute("cx",b[0]*xunitlength+origin[0]);c.setAttribute("cy",height-b[1]*yunitlength-origin[1]);c.setAttribute("r",a*xunitlength);c.setAttribute("stroke-width",strokewidth);c.setAttribute("stroke",stroke);c.setAttribute("fill",fill);c.setAttribute("stroke-opacity",strokeopacity);c.setAttribute("fill-opacity",fillopacity)}function loop(a,b,c){if(b==null){b=[1,0]}path([a,[a[0]+b[0],a[1]+b[1]],[a[0]-b[1],a[1]+b[0]],a],c,"C");if(marker=="arrow"||marker=="arrowdot"){arrowhead([a[0]+Math.cos(1.4)*b[0]-Math.sin(1.4)*b[1],a[1]+Math.sin(1.4)*b[0]+Math.cos(1.4)*b[1]],a)}}function arc(h,c,a,g,b){var f,d;if(g!=null){f=doc.getElementById(g)}if(b==null){b=0}if(a==null){d=[c[0]-h[0],c[1]-h[1]];a=Math.sqrt(d[0]*d[0]+d[1]*d[1])}if(f==null){f=myCreateElementSVG("path");f.setAttribute("id",g);svgpicture.appendChild(f)}f.setAttribute("d","M"+(h[0]*xunitlength+origin[0])+","+(height-h[1]*yunitlength-origin[1])+" A"+a*xunitlength+","+a*yunitlength+" 0 "+b+",0 "+(c[0]*xunitlength+origin[0])+","+(height-c[1]*yunitlength-origin[1]));f.setAttribute("stroke-width",strokewidth);f.setAttribute("stroke",stroke);f.setAttribute("fill",fill);f.setAttribute("stroke-opacity",strokeopacity);f.setAttribute("fill-opacity",fillopacity);if(marker=="arrow"||marker=="arrowdot"){u=[(c[1]-h[1])/4,(h[0]-c[0])/4];d=[(c[0]-h[0])/2,(c[1]-h[1])/2];d=[h[0]+d[0]+u[0],h[1]+d[1]+u[1]]}else{d=[h[0],h[1]]}if(marker=="dot"||marker=="arrowdot"){ASdot(h,markersize,markerstroke,markerfill);if(marker=="arrowdot"){arrowhead(d,c)}ASdot(c,markersize,markerstroke,markerfill)}else{if(marker=="arrow"){arrowhead(d,c)}}}function sector(a,g,b,f){var d=g[0]-a[0],c=g[1]-a[1];arc(g,b,Math.sqrt(d*d+c*c),f+"arc");path([b,a,g],f+"path")}function ellipse(a,d,c,f){var b;if(f!=null){b=doc.getElementById(f)}if(b==null){b=myCreateElementSVG("ellipse");b.setAttribute("id",f);svgpicture.appendChild(b)}b.setAttribute("cx",a[0]*xunitlength+origin[0]);b.setAttribute("cy",height-a[1]*yunitlength-origin[1]);b.setAttribute("rx",d*xunitlength);b.setAttribute("ry",c*yunitlength);b.setAttribute("stroke-width",strokewidth);b.setAttribute("stroke",stroke);b.setAttribute("fill",fill);b.setAttribute("stroke-opacity",strokeopacity);b.setAttribute("fill-opacity",fillopacity)}function triangle(c,b,a,d){path([c,b,a,c],d)}function rect(f,c,g,d,b){var a;if(g!=null){a=doc.getElementById(g)}if(a==null){a=myCreateElementSVG("rect");a.setAttribute("id",g);svgpicture.appendChild(a)}a.setAttribute("x",f[0]*xunitlength+origin[0]);a.setAttribute("y",height-c[1]*yunitlength-origin[1]);a.setAttribute("width",(c[0]-f[0])*xunitlength);a.setAttribute("height",(c[1]-f[1])*yunitlength);if(d!=null){a.setAttribute("rx",d*xunitlength)}if(b!=null){a.setAttribute("ry",b*yunitlength)}a.setAttribute("stroke-width",strokewidth);a.setAttribute("stroke",stroke);a.setAttribute("fill",fill);a.setAttribute("stroke-opacity",strokeopacity);a.setAttribute("fill-opacity",fillopacity)}function text(b,l,h,a,j){var f,d,m=0,k=fontsize/3,g=l.toString();if(/(`|\$)/.test(g)){f=document.getElementById(svgpicture.getAttribute("name")+"mml");if(f!=null){if(a!=null){d=document.getElementById(a)}if(d==null){d=createElementXHTML("div");d.setAttribute("id",a);d.style.position="absolute";f.appendChild(d)}while(d.childNodes.length>0){d.removeChild(d.lastChild)}d.appendChild(document.createTextNode(g));if(/`/.test(g)){AMprocessNode(d)}else{LMprocessNode(d)}m=-d.offsetWidth/2;k=-d.offsetHeight/2;if(h!=null){if(/above/.test(h)){k=-d.offsetHeight}if(/below/.test(h)){k=0}if(/right/.test(h)){m=0}if(/left/.test(h)){m=-d.offsetWidth}}d.style.left=""+(b[0]*xunitlength+origin[0]+m)+"px";d.style.top=""+(height-b[1]*yunitlength-origin[1]+k)+"px"}return b}var c="middle";if(h!=null){if(/above/.test(h)){k=-fontsize/2}if(/below/.test(h)){k=fontsize-0}if(/right/.test(h)){c="start";m=fontsize/4}if(/left/.test(h)){c="end";m=-fontsize/4}}if(a!=null){d=doc.getElementById(a)}if(d==null){d=myCreateElementSVG("text");d.setAttribute("id",a);svgpicture.appendChild(d);d.appendChild(doc.createTextNode(g))}while(d.childNodes.length>1){d.removeChild(d.lastChild)}d.lastChild.nodeValue="\xA0"+g+"\xA0";d.setAttribute("x",b[0]*xunitlength+origin[0]+m);d.setAttribute("y",height-b[1]*yunitlength-origin[1]+k);d.setAttribute("font-style",(j!=null?j:(g.search(/^[a-zA-Z]$/)!=-1?"italic":fontstyle)));d.setAttribute("font-family",fontfamily);d.setAttribute("font-size",fontsize);d.setAttribute("font-weight",fontweight);d.setAttribute("text-anchor",c);if(fontstroke!="none"){d.setAttribute("stroke",fontstroke)}if(fontfill!="none"){d.setAttribute("fill",fontfill)}return b}function mtext(a,h,d,g,f){var c="middle";var k=0;var j=fontsize/3;if(d!=null){if(d.slice(0,5)=="above"){j=-fontsize/2}if(d.slice(0,5)=="below"){j=fontsize-0}if(d.slice(0,5)=="right"||d.slice(5,10)=="right"){c="start";k=fontsize/2}if(d.slice(0,4)=="left"||d.slice(5,9)=="left"){c="end";k=-fontsize/2}}var b=this;if(this.nodeName=="svg"){b=myCreateElementSVG("text");this.appendChild(b);b.appendChild(doc.createTextNode(h))}b.lastChild.nodeValue=h;b.setAttribute("x",a[0]+k);b.setAttribute("y",a[1]+j);b.setAttribute("font-style",(g!=null?g:fontstyle));b.setAttribute("font-family",fontfamily);b.setAttribute("font-size",(f!=null?f:fontsize));b.setAttribute("font-weight",fontweight);b.setAttribute("text-anchor",c);if(fontstroke!="none"){b.setAttribute("stroke",fontstroke)}if(fontfill!="none"){b.setAttribute("fill",fontfill)}}function image(b,f,a,c,g){var d;if(g!=null){d=doc.getElementById(g)}if(d==null){d=myCreateElementSVG("image");d.setAttribute("id",g);svgpicture.appendChild(d)}d.setAttribute("x",f[0]*xunitlength+origin[0]);d.setAttribute("y",height-f[1]*yunitlength-origin[1]);d.setAttribute("width",a);d.setAttribute("height",c);d.setAttribute("xlink:href",b)}function ASdot(b,a,c,g){if(c==null){c=stroke}if(g==null){g=fill}var d=myCreateElementSVG("circle");d.setAttribute("cx",b[0]*xunitlength+origin[0]);d.setAttribute("cy",height-b[1]*yunitlength-origin[1]);d.setAttribute("r",a);d.setAttribute("stroke-width",strokewidth);d.setAttribute("stroke",c);d.setAttribute("fill",g);svgpicture.appendChild(d)}function dot(b,f,c,j,h){var d;var a=b[0]*xunitlength+origin[0];var g=height-b[1]*yunitlength-origin[1];if(h!=null){d=doc.getElementById(h)}if(f=="+"||f=="-"||f=="|"){if(d==null){d=myCreateElementSVG("path");d.setAttribute("id",h);svgpicture.appendChild(d)}if(f=="+"){d.setAttribute("d"," M "+(a-ticklength)+" "+g+" L "+(a+ticklength)+" "+g+" M "+a+" "+(g-ticklength)+" L "+a+" "+(g+ticklength));d.setAttribute("stroke-width",0.5);d.setAttribute("stroke",axesstroke)}else{if(f=="-"){d.setAttribute("d"," M "+(a-ticklength)+" "+g+" L "+(a+ticklength)+" "+g)}else{d.setAttribute("d"," M "+a+" "+(g-ticklength)+" L "+a+" "+(g+ticklength))}d.setAttribute("stroke-width",strokewidth);d.setAttribute("stroke",stroke)}}else{if(d==null){d=myCreateElementSVG("circle");d.setAttribute("id",h);svgpicture.appendChild(d)}d.setAttribute("cx",a);d.setAttribute("cy",g);d.setAttribute("r",dotradius);d.setAttribute("stroke-width",strokewidth);d.setAttribute("stroke",stroke);d.setAttribute("fill",(f=="open"?"white":(f=="closed"?stroke:markerfill)))}if(c!=null){text(b,c,(j==null?"below":j),(h==null?h:h+"label"))}}point=dot;function arrowhead(j,h){var a;var c=[j[0]*xunitlength+origin[0],height-j[1]*yunitlength-origin[1]];var b=[h[0]*xunitlength+origin[0],height-h[1]*yunitlength-origin[1]];var f=[b[0]-c[0],b[1]-c[1]];var k=Math.sqrt(f[0]*f[0]+f[1]*f[1]);if(k>1e-8){f=[f[0]/k,f[1]/k];a=[-f[1],f[0]];var g=myCreateElementSVG("path");g.setAttribute("d","M "+(b[0]-15*f[0]-4*a[0])+" "+(b[1]-15*f[1]-4*a[1])+" L "+(b[0]-3*f[0])+" "+(b[1]-3*f[1])+" L "+(b[0]-15*f[0]+4*a[0])+" "+(b[1]-15*f[1]+4*a[1])+" z");g.setAttribute("stroke-width",markerstrokewidth);g.setAttribute("stroke",stroke);g.setAttribute("fill",stroke);g.setAttribute("stroke-opacity",strokeopacity);g.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(g)}}function chopZ(b){var a=b.indexOf(".");if(a==-1){return b}for(var c=b.length-1;c>a&&b.charAt(c)=="0";c--){}if(c==a){c--}return b.slice(0,c+1)}function grid(b,a){axes(b,a,null,b,a)}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",0.5);pnode.setAttribute("stroke",gridstroke);pnode.setAttribute("fill",fill);svgpicture.appendChild(pnode)}pnode=myCreateElementSVG("path");st="M0,"+(height-origin[1])+" "+width+","+(height-origin[1])+" M"+origin[0]+",0 "+origin[0]+","+height;for(x=origin[0]+dx;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",0.5);pnode.setAttribute("stroke",axesstroke);pnode.setAttribute("fill",fill);pnode.setAttribute("stroke-opacity",strokeopacity);pnode.setAttribute("fill-opacity",fillopacity);svgpicture.appendChild(pnode)}function mathjs(c){c=c.replace(/\s/g,"");if(c.indexOf("^-1")!=-1){c=c.replace(/sin\^-1/g,"arcsin");c=c.replace(/cos\^-1/g,"arccos");c=c.replace(/tan\^-1/g,"arctan");c=c.replace(/sec\^-1/g,"arcsec");c=c.replace(/csc\^-1/g,"arccsc");c=c.replace(/cot\^-1/g,"arccot");c=c.replace(/sinh\^-1/g,"arcsinh");c=c.replace(/cosh\^-1/g,"arccosh");c=c.replace(/tanh\^-1/g,"arctanh");c=c.replace(/sech\^-1/g,"arcsech");c=c.replace(/csch\^-1/g,"arccsch");c=c.replace(/coth\^-1/g,"arccoth")}c=c.replace(/^e$/g,"(Math.E)");c=c.replace(/^e([^a-zA-Z])/g,"(Math.E)$1");c=c.replace(/([^a-zA-Z])e/g,"$1(Math.E)");c=c.replace(/([0-9])([\(a-zA-Z])/g,"$1*$2");c=c.replace(/\)([\(0-9a-zA-Z])/g,")*$1");var d,b,a,f,g;while((d=c.indexOf("^"))!=-1){if(d==0){return"Error: missing argument"}b=d-1;f=c.charAt(b);if(f>="0"&&f<="9"){b--;while(b>=0&&(f=c.charAt(b))>="0"&&f<="9"){b--}if(f=="."){b--;while(b>=0&&(f=c.charAt(b))>="0"&&f<="9"){b--}}}else{if(f==")"){g=1;b--;while(b>=0&&g>0){f=c.charAt(b);if(f=="("){g--}else{if(f==")"){g++}}b--}while(b>=0&&(f=c.charAt(b))>="a"&&f<="z"||f>="A"&&f<="Z"){b--}}else{if(f>="a"&&f<="z"||f>="A"&&f<="Z"){b--;while(b>=0&&(f=c.charAt(b))>="a"&&f<="z"||f>="A"&&f<="Z"){b--}}else{return"Error: incorrect syntax in "+c+" at position "+b}}}if(d==c.length-1){return"Error: missing argument"}a=d+1;f=c.charAt(a);if(f>="0"&&f<="9"||f=="-"){a++;while(a<c.length&&(f=c.charAt(a))>="0"&&f<="9"){a++}if(f=="."){a++;while(a<c.length&&(f=c.charAt(a))>="0"&&f<="9"){a++}}}else{if(f=="("){g=1;a++;while(a<c.length&&g>0){f=c.charAt(a);if(f=="("){g++}else{if(f==")"){g--}}a++}}else{if(f>="a"&&f<="z"||f>="A"&&f<="Z"){a++;while(a<c.length&&(f=c.charAt(a))>="a"&&f<="z"||f>="A"&&f<="Z"){a++}}else{return"Error: incorrect syntax in "+c+" at position "+a}}}c=c.slice(0,b+1)+"Math.pow("+c.slice(b+1,d)+","+c.slice(d+1,a)+")"+c.slice(a)}while((d=c.indexOf("!"))!=-1){if(d==0){return"Error: missing argument"}b=d-1;f=c.charAt(b);if(f>="0"&&f<="9"){b--;while(b>=0&&(f=c.charAt(b))>="0"&&f<="9"){b--}if(f=="."){b--;while(b>=0&&(f=c.charAt(b))>="0"&&f<="9"){b--}}}else{if(f==")"){g=1;b--;while(b>=0&&g>0){f=c.charAt(b);if(f=="("){g--}else{if(f==")"){g++}}b--}while(b>=0&&(f=c.charAt(b))>="a"&&f<="z"||f>="A"&&f<="Z"){b--}}else{if(f>="a"&&f<="z"||f>="A"&&f<="Z"){b--;while(b>=0&&(f=c.charAt(b))>="a"&&f<="z"||f>="A"&&f<="Z"){b--}}else{return"Error: incorrect syntax in "+c+" at position "+b}}}c=c.slice(0,b+1)+"factorial("+c.slice(b+1,d)+")"+c.slice(d+1)}return c}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(c){var a="";for(var b=0;b<c.childNodes.length;b++){a+=c.childNodes.item(b)+"\n"}return a}function displayCoord(b){if(showcoordinates){var d=b.target.parentNode;var a=d.childNodes;for(var c=0;c<a.length&&a.item(c).nodeName!="text";c++){}var f=a.item(c);f.mtext=mtext;f.mtext([d.getAttribute("width")-(-7),d.getAttribute("height")-7],"("+getX(b).toFixed(2)+", "+getY(b).toFixed(2)+")","left","","11")}}function removeCoord(b){var d=b.target.parentNode;var a=d.childNodes;for(var c=0;c<a.length&&a.item(c).nodeName!="text";c++){}var f=a.item(c);f.mtext=mtext;f.mtext([d.getAttribute("width")-0,d.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(a){document.getElementById("in").value+=a;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 b=document.getElementById("processasciimathinmoodle");if(b!=null){dsvglocation=b.className}if(b!=null||!checkforprocessasciimathinmoodle){translate();if(!noSVG&&translateASCIIsvg){drawPictures()}}var a=getElementsByClass(document,"div","ASCIIMathCalculator");if(!noMathML&&a.length>0){initASCIIMathCalculators(a)}}}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}}}};