",TITLE,"

var Phi=(Math.sqrt(5)+1)/2, phi=Phi-1; function DoERROR(){return false}; function resetERROR(){self.onerror=DoERROR;return true}; function HALT(msg){alert("**Problem**\r"+msg);self.onerror=resetERROR;ERROR();alert("aagh - after HALT")}; var ErrorAt="",ErrorIn=""; function ERRORHandler(msg,error,line){alert("There is a problem with "+ErrorAt+":\r"+ErrorIn+" is not a number.");return true}; // Make a window Pop Up var debug=false,record=false; var _auxwin; if(debug){_auxwin=window.open("","tip","width=500,height=400,scrollbars=yes,resizable=yes,status=yes"); _auxwin.document.open("text/plain") }; function _AuxWinOpen(typ){ //default typ=="html" //alert(typ); _auxwin=window.open("","tip","width=500,height=400,scrollbars=yes,resizable=yes,status=yes"); //if already open, does nothing //if(typ && typ=="plain"){_auxwin.document.open("text/plain")}else{_auxwin.document.open()}; _auxwin.focus() }; function DBG(args){ //no args means clear _auxwin window if(!debug)return; if(arguments.length==0){_auxwin.document.close();_auxwin.document.open("text/plain");} else {for(var i=0;i0?"+":k<0?"-":"") +(Math.abs(k)!=1?Math.abs(k):"") +"sqrt("+n+")" :""); return (s!=1 ? (n==0||r==0?"":"(") : "") + top + (s!=1 ? (n==0||r==0?"":")") : "") +(s==1?"":"/"+s) }; function showrnsdc(r,n,s,d,c){ if(debug)DBG("showrnsdc("+r+","+n+","+s+","+d+","+c+")"); var k=(n!=0?Math.sqrt(sqrfactor(n)):1); var nk=(k!=1?Math.round(n/k/k):n); // ASSERT sqrt(n) = k sqrt(nn) if(s<0){s= -s;r=-r;k=-k} return (r!=0||n!=0||s!=1?showrns(r,(k<0?-1:1),n,s) +(k!=1&&k!=-1&&nk!=1?" = "+showrns(r,k,nk,s):"")+" = ":"") +d+(c!=d?" = "+c:"") }; function recrd(){ // if(!document.ans.Record.checked)return; var rns=getRNS(); var r=rns.R,n=rns.N,s=rns.S, d=document.f.dec.value, c=Cf.cftoString(); document.ans.Recordtxt.value = document.ans.Recordtxt.value +showrnsdc(r,n,s,d,c) +"\r"; }; function _AuxWinHTML(lines){ var TITLE="",i=0; _AuxWinOpen("html"); if(beginswith(arguments[0],"OPT")){i=1;eval(arguments[0].substring(3))}; with(_auxwin.document) {writeln("",TITLE,""); for(i;i

", "", "

") }; _auxwin.document.close() } function _AuxWinPlain(msg){ _AuxWinOpen("plain"); with(_auxwin.document) for(var i=0;i=0, b>=0 if(a==0) return b else if(b==0) return a else return gcd1(b%a,a) }; function isINT(v,txt,e){var i; v=v.replace(/,/g,"").replace(/\s/g,""); if(v.indexOf(".")!=-1)HALT(txt+" must be a whole number.\rUse the 'Decimal:' box for decimal number values."); if(v==""){if(arguments.length>=3){return e}else{return Number.NaN}}; ErrorAt=txt;ErrorIn=v;self.onerror=ERRORHandler;i=eval(v);self.onerror=DoERROR; if(isNaN(i))HALT(txt+" is not a number."); if(i.toString()!=v && v.replace(/\d/g,"")=="")HALT("The number "+txt+" is too long:\r"+v); return i }; function isREAL(v,txt,e){ v=v.replace(/,/g,"").replace(/\s/g,""); if(v==""){if(arguments.length>=3){return e}else{return Number.NaN}}; var r=parseFloat(v); if(isNaN(r))HALT(txt+" is not a number."); return r }; function justify(s,fw,opt){var i; if(typeof s != "string")s=s.toString(); if(arguments.length<3)opt="L"; if(opt=="L")for(i=s.length;i=ii && i<=lim;i=i+2,ii=i*i) {//if(debug)DBG("sqrf i="+i+" ii="+ii+" n="+n); while(n>=ii && n%ii==0){f=f*ii;n=Math.round(n/ii) //if(debug)DBG(" ..f="+f+" n="+n) }}; if(debug)DBG("sqrfactor of "+N+" = "+f+" *"+n); return f }; function simplifyrns(r,n,s){ //check for common factors... // var FF=sqrfactor(n);var F=Math.round(Math.sqrt(FF)); //n=F*F*(n/FF) var g=gcd(r,Math.round(Math.sqrt(sqrfactor(gcd(n,s*s))))); if(debug)DBG("r="+r+" n="+n+" s="+s+" g="+g); r=Math.round(r/g);s=Math.round(s/g);n=Math.round(n/(g*g)); return [r,n,s] } function sqrtSHOW(r,n,s){ var rns=simplifyrns(r,n,s); r=rns[0];n=rns[1];s=rns[2]; setRNS(r,n,s); Sqrt2Dec(); }; function evalDec(){var v; try { with(Math){ v=eval(document.f.dec.value.replace(/Pi/ig,"PI") )}; }catch(e){HALT(" The decimal expression cannot be evaluated - please correct it")}; if(typeof v == "undefined")HALT(" Please type a number into the Decimal box"); if(v<0)HALT("Decimal Value is negative"); if(!isFinite(v))HALT("The decimal is too large - sorry"); if(v==0)HALT("The decimal value is too small - sorry"); if(v!=document.f.dec.value) document.ans.Recordtxt.value = document.ans.Recordtxt.value+document.f.dec.value+" = "; document.f.dec.value=v }; function rat2cf(r,s){ // r/s var t=r,b=s,i=-1,q; Cf.reset(); do{ q=CFtrunc(t/b); r=t-q*b; Cf.append(q); t=b;b=r; } while (r/=0 && !Cf.stopped); }; function Rat2CF(r,s){ //ASSERT n = 0 if(debug)DBG("Rat2CF("+r+","+s+")"); if(arguments.length==0) {var rnsin=getRNS();r=rnsin.R;s=rnsin.S} var g=gcd(r,s); if(g>1){document.ans.Recordtxt.value=document.ans.Recordtxt.value+r+"/"+s+" = "; r=Math.round(r/g);s=Math.round(s/g); setRNS(r,0,s)}; rat2cf(r,s); cfSHOW(); }; function Real2CF(){ var i=-1; Cf.reset(); clearxcpt('dec'); var r=isREAL(document.f.dec.value,"Your Decimal entry"),q; if(isNaN(r))return; if(r<0)HALT("Decimal value is negative"); do { q=CFtrunc(r); if(isFinite(q)){Cf.append(q); r=1/(r-q)}; } while(!Cf.stopped && isFinite(r)); cfSHOW(); recrd(); }; function Sqrt2Dec(r,n,s){ //alert("Sqrt2Dec"); if(arguments.length==0) {var rnsin=getRNS(); r=rnsin.R;n=rnsin.N;s=rnsin.S }; var v=(r+Math.sqrt(n))/s; if(v<0)HALT("The fraction is negative:"+v); document.f.dec.value=v; if(debug)DBG("_____Sqrt to Dec ____ ("+r+" +sqrt "+n+")/"+s+" = "+document.f.dec.value) }; function Sqrt2CF(){ var rnsin=getRNS();var r=rnsin.R,n=rnsin.N,s=rnsin.S; Sqrt2Dec(r,n,s); if(n==0){Rat2CF(r,s)} else{SqrtPeriodicCF(r,n,s)}; recrd(); }; function SqrtPeriodicCF(r,n,s){ if(arguments.length==0) {var rnsin=getRNS();r=rnsin.R;n=rnsin.N;s=rnsin.S}; Cf.reset(); var R=new Array();R[0]=r; var S=new Array();S[0]=s; var sqt=Math.floor(Math.sqrt(n)); if(sqt*sqt==n) {Rat2CF(r+sqt,s)} else { if(n-R[0]*R[0] % S[0] !=0){R[0]=R[0]*Math.abs(S[0]);n=n*S[0]*S[0];S[0]=S[0]*Math.abs(S[0])}; var j=0; for(i=1;j==0 && !Cf.cfOFLO;i++) {Cf.append(Math.floor((R[i-1]+Math.sqrt(n))/S[i-1])); R[i]=Cf.lastcf()*S[i-1]-R[i-1]; S[i]=(n-R[i]*R[i])/S[i-1]; for(j=i-1;j>0 && (R[j]!=R[i] || S[j]!=S[i]);j--){}; }; if(!Cf.cfOFLO){Cf.cfperiodLWB=j;Cf.cfperiodUPB=i-2} while(!Cf.stopped)Cf.append(Cf.cf[j++]); }; cfSHOW(); if(debug)DBG("______Sqrt to CF_____\r"+Cf.toString()+"\r"+document.f.dec.value+" ("+eval((-r+Math.sqrt(n))/-s)+")"); }; function updateCF(){ var cf=document.f.cf.value.replace(/\.\.\./,"").replace(/\s/g,"").replace(/;/,','); var e=cf.replace(/\[/,"").replace(/\]/,"").replace(/,/g,"").replace(/\d/g,""); if(e.replace(/[-\.]/g,"")!="") HALT("Your CF must contain ONLY numbers separated by , with '[' and ']' to show any period.\r I found "+e); cf=eval("["+cf+"]"); Cf.reset(); for(var i=0;i0) HALT("Only the first number in your CF can be 0.") else if(cf[i]<0) HALT("You cannot have negative numbers in your CF.\rI found "+cf[i]) else Cf.append(cf[i]); i=cf.length-1; if(typeof cf[i] != "object"){Cf.append(cf[i])} else {Cf.cfperiodLWB=i; for(j=0;jMath.abs(d2-dd)){r=-r;s=-s;pdec=d2} if(debug)DBG(" and nearest to ",dd," is r=",r," s=",s); //----INITIAL NON-PERIODIC PART--------- if(Cf.cfperiodLWB>0) {for(i=0;iMath.abs(Dec2-truedec)) {R=-R;S=-S}; } else{R=r;N=n;S=s}; sqrtSHOW(R,N,S); if(debug)DBG("___dec showing___ "+document.f.dec.value); }; function CFalt(){ //alert("CFalt "+cf.length+" elts;last is ="+cf[cf.length-1]+(cf[cf.length-1]==1)); //document.ans.Recordtxt.value = document.ans.Recordtxt.value+Cf.dump(); if(Cf.isPeriodic()){alert("Periodic (infinite) CFs do not have an alternative ending");return}; Cf.altcf(); cfSHOW(); }; function egSHOW(){ var which=document.f.eg[document.f.eg.selectedIndex].value; if(which==""){alert("Use the '"+document.f.eg[0].value+"' selector to choose which kind of example.")} else if(which=="egfr"){setRNS(3,0,50); clearxcpt('fract'); pushme(document.ratRbtn)} else if(which=="egdec"){document.f.dec.value="0.123456790123";clearxcpt('dec');pushme(document.decRbtn);} else if(which=="egpi"){document.f.dec.value="pi";clearxcpt('dec');pushme(document.decRbtn);} else if(which=="egsqrt"){setRNS(0,6,1);clearxcpt('fract');pushme(document.ratRbtn);} else if(which=="egcfrat1"){document.f.cf.value="0,1,2,3";clearxcpt('cf'); pushme(document.cfLbtn);document.ans.morecf.value=" ";} else if(which=="egcfrat2"){document.f.cf.value="4,3,[1,2]";clearxcpt('cf'); pushme(document.cfLbtn);document.ans.morecf.value=" ";} else if(which=="egeval1"){document.f.dec.value="3*4.5 - 7.6/8";clearxcpt('dec');pushme(document.decRbtn)} else if(which=="egeval2"){document.f.dec.value="pow((sqrt(5)+1)/2,3)";clearxcpt('dec');pushme(document.decRbtn)} else if(which=="egeval3"){document.f.dec.value="cos(Pi*36/180)";clearxcpt('dec');pushme(document.decRbtn)} }; function clearxcpt(fld){ if(arguments.length==0)fld=""; eval(btnoff); if(fld!='cf') {document.f.cf.value=" ";document.ans.morecf.value=" "; Cf.reset();}; if(fld!="dec") {document.f.dec.value=""} if(fld!="fract"){setRNS("","","")} }; var btnoff=""; function pushme(wh){ //alert(wh.name+" "+wh.src); if(endswith(wh.src,"HiLite.gif")) {wh.src= wh.src.replace(/HiLite/,'');btnoff=""} else {wh.src= wh.src.replace(/\.gif/,"HiLite.gif");btnoff="pushme(document."+wh.name+")"} ; }; function dogcd(){ if(document.f.g1.value=="")return; if(document.f.g2.value=="")return; document.f.gcd12.value=gcd(document.f.g1.value,document.f.g2.value) }; function dps(r,d){ var x= (Math.floor(r*Math.pow(10,d))/Math.pow(10,d)).toString(); for(var i=1;x.length-x.indexOf(".")-1Math.abs(real-t/b)) {bestt=t;bestb=b;approxs[approxs.length]=new RAT(t,b) rat2cf(t,b); err=eval(t/b)-real; document.ans.Recordtxt.value+="\r"+dps(eval(t/b),maxd+3)+"="+t+"/"+b+"="+Cf.cftoString()+" err="+err} }; document.ans.Recordtxt.value+="\r"; return approxs };