var aa;var ba=0xdeadbeefcafe;var ca=((ba&0xffffff)==0xefcafe);function da(a,b,c){if(a!=null)if("number"==typeof a)this.fromNumber(a,b,c);else if(b==null&&"string"!=typeof a)this.fromString(a,256);else this.fromString(a,b);}function ea(){return new da(null);}function fa(i,x,w,j,c,n){while(--n>=0){var v=x*this[i++]+w[j]+c;c=Math.floor(v/0x4000000);w[j++]=v&0x3ffffff;}return c;}function ga(i,x,w,j,c,n){var ha=x&0x7fff,ia=x>>15;while(--n>=0){var l=this[i]&0x7fff;var h=this[i++]>>15;var m=ia*l+h*ha;l=ha*l+((m&0x7fff)<<15)+w[j]+(c&0x3fffffff);c=(l>>>30)+(m>>>15)+ia*h+(c>>>30);w[j++]=l&0x3fffffff;}return c;}function ja(i,x,w,j,c,n){var ha=x&0x3fff,ia=x>>14;while(--n>=0){var l=this[i]&0x3fff;var h=this[i++]>>14;var m=ia*l+h*ha;l=ha*l+((m&0x3fff)<<14)+w[j]+c;c=(l>>28)+(m>>14)+ia*h;w[j++]=l&0xfffffff;}return c;}if(ca&&(navigator.appName=="Microsoft Internet Explorer")){da.prototype.am=ga;aa=30;}else if(ca&&(navigator.appName!="Netscape")){da.prototype.am=fa;aa=26;}else{da.prototype.am=ja;aa=28;}da.prototype.DB=aa;da.prototype.DM=((1<=0;--i)r[i]=this[i];r.t=this.t;r.s=this.s;}function sa(x){this.t=1;this.s=(x<0)?-1:0;if(x>0)this[0]=x;else if(x<-1)this[0]=x+ta;else this.t=0;}function ua(i){var r=ea();r.fromInt(i);return r;}function va(s,b){var k;if(b==16)k=4;else if(b==8)k=3;else if(b==256)k=8;else if(b==2)k=1;else if(b==32)k=5;else if(b==4)k=2;else{this.fromRadix(s,b);return;}this.t=0;this.s=0;var i=s.length,wa=false,xa=0;while(--i>=0){var x=(k==8)?s[i]&0xff:qa(s,i);if(x<0){if(s.charAt(i)=="-")wa=true;continue;}wa=false;if(xa==0)this[this.t++]=x;else if(xa+k>this.DB){this[this.t-1]|=(x&((1<<(this.DB-xa))-1))<>(this.DB-xa));}else this[this.t-1]|=x<=this.DB)xa-=this.DB;}if(k==8&&(s[0]&0x80)!=0){this.s=-1;if(xa>0)this[this.t-1]|=((1<<(this.DB-xa))-1)<0&&this[this.t-1]==c)--this.t;}function za(b){if(this.s<0)return"-"+this.negate().toString(b);var k;if(b==16)k=4;else if(b==8)k=3;else 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i=n;i=0;--i){r[i+Ma+1]=(this[i]>>Ka)|c;c=(this[i]&La)<=0;--i)r[i]=0;r[Ma]=c;r.t=this.t+Ma+1;r.s=this.s;r.clamp();}function Na(n,r){r.s=this.s;var Ma=Math.floor(n/this.DB);if(Ma>=this.t){r.t=0;return;}var Ja=n%this.DB;var Ka=this.DB-Ja;var La=(1<>Ja;for(var i=Ma+1;i>Ja;}if(Ja>0)r[this.t-Ma-1]|=(this.s&La)<>=this.DB;}if(a.t>=this.DB;}c+=this.s;}else{c+=this.s;while(i>=this.DB;}c-=a.s;}r.s=(c<0)?-1:0;if(c<-1)r[i++]=this.DV+c;else if(c>0)r[i++]=c;r.t=i;r.clamp();}function Pa(a,r){var x=this.abs(),y=a.abs();var i=x.t;r.t=i+y.t;while(--i>=0)r[i]=0;for(i=0;i=0)r[i]=0;for(i=0;i=x.DV){r[i+x.t]-=x.DV;r[i+x.t+1]=1;}}if(r.t>0)r[r.t-1]+=x.am(i,x[i],r,2*i,0,1);r.s=0;r.clamp();}function Ra(m,q,r){var Sa=m.abs();if(Sa.t<=0)return;var Ta=this.abs();if(Ta.t0){Sa.lShiftTo(Wa,y);Ta.lShiftTo(Wa,r);}else{Sa.copyTo(y);Ta.copyTo(r);}var Xa=y.t;var Ya=y[Xa-1];if(Ya==0)return;var Za=Ya*(1<1)?y[Xa-2]>>this.F2:0);var ab=this.FV/Za,bb=(1<=0){r[r.t++]=1;r.subTo(t,r);}da.ONE.dlShiftTo(Xa,t);t.subTo(y,y);while(y.t=0){var cb=(r[--i]==Ya)?this.DM:Math.floor(r[i]*ab+(r[i-1]+e)*bb);if((r[i]+=y.am(0,cb,r,j,0,Xa))0)r.rShiftTo(Wa,r);if(Ua<0)da.ZERO.subTo(r,r);}function db(a){var r=ea();this.abs().divRemTo(a,null,r);if(this.s<0&&r.compareTo(da.ZERO)>0)a.subTo(r,r);return r;}function eb(m){this.m=m;}function fb(x){if(x.s<0||x.compareTo(this.m)>=0)return x.mod(this.m);else return x;}function gb(x){return x;}function hb(x){x.divRemTo(this.m,null,x);}function ib(x,y,r){x.multiplyTo(y,r);this.reduce(r);}function jb(x,r){x.squareTo(r);this.reduce(r);}eb.prototype.convert=fb;eb.prototype.revert=gb;eb.prototype.reduce=hb;eb.prototype.mulTo=ib;eb.prototype.sqrTo=jb;function kb(){if(this.t<1)return 0;var x=this[0];if((x&1)==0)return 0;var y=x&3;y=(y*(2-(x&0xf)*y))&0xf;y=(y*(2-(x&0xff)*y))&0xff;y=(y*(2-(((x&0xffff)*y)&0xffff)))&0xffff;y=(y*(2-x*y%this.DV))%this.DV;return(y>0)?this.DV-y:-y;}function lb(m){this.m=m;this.mp=m.invDigit();this.mpl=this.mp&0x7fff;this.mph=this.mp>>15;this.um=(1<<(m.DB-15))-1;this.mt2=2*m.t;}function mb(x){var r=ea();x.abs().dlShiftTo(this.m.t,r);r.divRemTo(this.m,null,r);if(x.s<0&&r.compareTo(da.ZERO)>0)this.m.subTo(r,r);return r;}function nb(x){var r=ea();x.copyTo(r);this.reduce(r);return r;}function ob(x){while(x.t<=this.mt2)x[x.t++]=0;for(var i=0;i>15)*this.mpl)&this.um)<<15))&x.DM;j=i+this.m.t;x[j]+=this.m.am(0,pb,x,i,0,this.m.t);while(x[j]>=x.DV){x[j]-=x.DV;x[++j]++;}}x.clamp();x.drShiftTo(this.m.t,x);if(x.compareTo(this.m)>=0)x.subTo(this.m,x);}function qb(x,r){x.squareTo(r);this.reduce(r);}function rb(x,y,r){x.multiplyTo(y,r);this.reduce(r);}lb.prototype.convert=mb;lb.prototype.revert=nb;lb.prototype.reduce=ob;lb.prototype.mulTo=rb;lb.prototype.sqrTo=qb;function sb(){return((this.t>0)?(this[0]&1):this.s)==0;}function tb(e,z){if(e>0xffffffff||e<1)return da.ONE;var r=ea(),ub=ea(),g=z.convert(this),i=Ea(e)-1;g.copyTo(r);while(--i>=0){z.sqrTo(r,ub);if((e&(1<0)z.mulTo(ub,g,r);else{var t=r;r=ub;ub=t;}}return z.revert(r);}function vb(e,m){var z;if(e<256||m.isEven())z=new eb(m);else z=new lb(m);return this.exp(e,z);}da.prototype.copyTo=ra;da.prototype.fromInt=sa;da.prototype.fromString=va;da.prototype.clamp=ya;da.prototype.dlShiftTo=Ga;da.prototype.drShiftTo=Ha;da.prototype.lShiftTo=Ia;da.prototype.rShiftTo=Na;da.prototype.subTo=Oa;da.prototype.multiplyTo=Pa;da.prototype.squareTo=Qa;da.prototype.divRemTo=Ra;da.prototype.invDigit=kb;da.prototype.isEven=sb;da.prototype.exp=tb;da.prototype.toString=za;da.prototype.negate=Ba;da.prototype.abs=Ca;da.prototype.compareTo=Da;da.prototype.bitLength=Fa;da.prototype.mod=db;da.prototype.modPowInt=vb;da.ZERO=ua(0);da.ONE=ua(1);function wb(){var r=ea();this.copyTo(r);return r;}function xb(){if(this.s<0){if(this.t==1)return this[0]-this.DV;else if(this.t==0)return-1;}else if(this.t==1)return this[0];else if(this.t==0)return 0;return((this[1]&((1<<(32-this.DB))-1))<>24;}function zb(){return(this.t==0)?this.s:(this[0]<<16)>>16;}function Ab(r){return Math.floor(Math.LN2*this.DB/Math.log(r));}function Bb(){if(this.s<0)return-1;else if(this.t<=0||(this.t==1&&this[0]<=0))return 0;else return 1;}function Cb(b){if(b==null)b=10;if(this.signum()==0||b<2||b>36)return"0";var Db=this.chunkSize(b);var a=Math.pow(b,Db);var d=ua(a),y=ea(),z=ea(),r="";this.divRemTo(d,y,z);while(y.signum()>0){r=(a+z.intValue()).toString(b).substr(1)+r;y.divRemTo(d,y,z);}return z.intValue().toString(b)+r;}function Eb(s,b){this.fromInt(0);if(b==null)b=10;var Db=this.chunkSize(b);var d=Math.pow(b,Db),wa=false,j=0,w=0;for(var i=0;i=Db){this.dMultiply(d);this.dAddOffset(w,0);j=0;w=0;}}if(j>0){this.dMultiply(Math.pow(b,j));this.dAddOffset(w,0);}if(wa)da.ZERO.subTo(this,this);}function Fb(a,b,c){if("number"==typeof b){if(a<2)this.fromInt(1);else{this.fromNumber(a,c);if(!this.testBit(a-1))this.bitwiseTo(da.ONE.shiftLeft(a-1),Gb,this);if(this.isEven())this.dAddOffset(1,0);while(!this.isProbablePrime(b)){this.dAddOffset(2,0);if(this.bitLength()>a)this.subTo(da.ONE.shiftLeft(a-1),this);}}}else{var x=new Array(),t=a&7;x.length=(a>>3)+1;b.nextBytes(x);if(t>0)x[0]&=((1<0){if(p>p)!=(this.s&this.DM)>>p)r[k++]=d|(this.s<<(this.DB-p));while(i>=0){if(p<8){d=(this[i]&((1<>(p+=this.DB-8);}else{d=(this[i]>>(p-=8))&0xff;if(p<=0){p+=this.DB;--i;}}if((d&0x80)!=0)d|=-256;if(k==0&&(this.s&0x80)!=(d&0x80))++k;if(k>0||d!=this.s)r[k++]=d;}}return r;}function Ib(a){return(this.compareTo(a)==0);}function Jb(a){return(this.compareTo(a)<0)?this:a;}function Kb(a){return(this.compareTo(a)>0)?this:a;}function Lb(a,Mb,r){var i,f,m=Math.min(a.t,this.t);for(i=0;i>=16;r+=16;}if((x&0xff)==0){x>>=8;r+=8;}if((x&0xf)==0){x>>=4;r+=4;}if((x&3)==0){x>>=2;r+=2;}if((x&1)==0)++r;return r;}function Yb(){for(var i=0;i=this.t)return(this.s!=0);return((this[j]&(1<<(n%this.DB)))!=0);}function cc(n,Mb){var r=da.ONE.shiftLeft(n);this.bitwiseTo(r,Mb,r);return r;}function dc(n){return this.changeBit(n,Gb);}function ec(n){return this.changeBit(n,Sb);}function fc(n){return this.changeBit(n,Qb);}function gc(a,r){var i=0,c=0,m=Math.min(a.t,this.t);while(i>=this.DB;}if(a.t>=this.DB;}c+=this.s;}else{c+=this.s;while(i>=this.DB;}c+=a.s;}r.s=(c<0)?-1:0;if(c>0)r[i++]=c;else if(c<-1)r[i++]=this.DV+c;r.t=i;r.clamp();}function hc(a){var r=ea();this.addTo(a,r);return r;}function ic(a){var r=ea();this.subTo(a,r);return r;}function jc(a){var r=ea();this.multiplyTo(a,r);return r;}function kc(a){var r=ea();this.divRemTo(a,r,null);return r;}function lc(a){var r=ea();this.divRemTo(a,null,r);return r;}function mc(a){var q=ea(),r=ea();this.divRemTo(a,q,r);return new Array(q,r);}function nc(n){this[this.t]=this.am(0,n-1,this,0,0,this.t);++this.t;this.clamp();}function oc(n,w){while(this.t<=w)this[this.t++]=0;this[w]+=n;while(this[w]>=this.DV){this[w]-=this.DV;if(++w>=this.t)this[this.t++]=0;++this[w];}}function pc(){}function qc(x){return x;}function rc(x,y,r){x.multiplyTo(y,r);}function sc(x,r){x.squareTo(r);}pc.prototype.convert=qc;pc.prototype.revert=qc;pc.prototype.mulTo=rc;pc.prototype.sqrTo=sc;function tc(e){return this.exp(e,new pc());}function uc(a,n,r){var i=Math.min(this.t+a.t,n);r.s=0;r.t=i;while(i>0)r[--i]=0;var j;for(j=r.t-this.t;i=0)r[i]=0;for(i=Math.max(n-this.t,0);i2*this.m.t)return x.mod(this.m);else if(x.compareTo(this.m)<0)return x;else{var r=ea();x.copyTo(r);this.reduce(r);return r;}}function yc(x){return x;}function zc(x){x.drShiftTo(this.m.t-1,this.r2);if(x.t>this.m.t+1){x.t=this.m.t+1;x.clamp();}this.mu.multiplyUpperTo(this.r2,this.m.t+1,this.q3);this.m.multiplyLowerTo(this.q3,this.m.t+1,this.r2);while(x.compareTo(this.r2)<0)x.dAddOffset(1,this.m.t+1);x.subTo(this.r2,x);while(x.compareTo(this.m)>=0)x.subTo(this.m,x);}function Ac(x,r){x.squareTo(r);this.reduce(r);}function Bc(x,y,r){x.multiplyTo(y,r);this.reduce(r);}wc.prototype.convert=xc;wc.prototype.revert=yc;wc.prototype.reduce=zc;wc.prototype.mulTo=Bc;wc.prototype.sqrTo=Ac;function Cc(e,m){var i=e.bitLength(),k,r=ua(1),z;if(i<=0)return r;else if(i<18)k=1;else if(i<48)k=3;else if(i<144)k=4;else if(i<768)k=5;else k=6;if(i<8)z=new eb(m);else if(m.isEven())z=new wc(m);else z=new lb(m);var g=new Array(),n=3,Dc=k-1,Aa=(1<1){var Ec=ea();z.sqrTo(g[1],Ec);while(n<=Aa){g[n]=ea();z.mulTo(Ec,g[n-2],g[n]);n+=2;}}var j=e.t-1,w,Fc=true,ub=ea(),t;i=Ea(e[j])-1;while(j>=0){if(i>=Dc)w=(e[j]>>(i-Dc))&Aa;else{w=(e[j]&((1<<(i+1))-1))<<(Dc-i);if(j>0)w|=e[j-1]>>(this.DB+i-Dc);}n=k;while((w&1)==0){w>>=1;--n;}if((i-=n)<0){i+=this.DB;--j;}if(Fc){g[w].copyTo(r);Fc=false;}else{while(n>1){z.sqrTo(r,ub);z.sqrTo(ub,r);n-=2;}if(n>0)z.sqrTo(r,ub);else{t=r;r=ub;ub=t;}z.mulTo(ub,g[w],r);}while(j>=0&&(e[j]&(1<0){x.rShiftTo(g,x);y.rShiftTo(g,y);}while(x.signum()>0){if((i=x.getLowestSetBit())>0)x.rShiftTo(i,x);if((i=y.getLowestSetBit())>0)y.rShiftTo(i,y);if(x.compareTo(y)>=0){x.subTo(y,x);x.rShiftTo(1,x);}else{y.subTo(x,y);y.rShiftTo(1,y);}}if(g>0)y.lShiftTo(g,y);return y;}function Hc(n){if(n<=0)return 0;var d=this.DV%n,r=(this.s<0)?n-1:0;if(this.t>0)if(d==0)r=this[0]%n;else for(var i=this.t-1;i>=0;--i)r=(d*r+this[i])%n;return r;}function Ic(m){var Jc=m.isEven();if((this.isEven()&&Jc)||m.signum()==0)return da.ZERO;var u=m.clone(),v=this.clone();var a=ua(1),b=ua(0),c=ua(0),d=ua(1);while(u.signum()!=0){while(u.isEven()){u.rShiftTo(1,u);if(Jc){if(!a.isEven()||!b.isEven()){a.addTo(this,a);b.subTo(m,b);}a.rShiftTo(1,a);}else if(!b.isEven())b.subTo(m,b);b.rShiftTo(1,b);}while(v.isEven()){v.rShiftTo(1,v);if(Jc){if(!c.isEven()||!d.isEven()){c.addTo(this,c);d.subTo(m,d);}c.rShiftTo(1,c);}else if(!d.isEven())d.subTo(m,d);d.rShiftTo(1,d);}if(u.compareTo(v)>=0){u.subTo(v,u);if(Jc)a.subTo(c,a);b.subTo(d,b);}else{v.subTo(u,v);if(Jc)c.subTo(a,c);d.subTo(b,d);}}if(v.compareTo(da.ONE)!=0)return da.ZERO;if(d.compareTo(m)>=0)return d.subtract(m);if(d.signum()<0)d.addTo(m,d);else return d;if(d.signum()<0)return d.add(m);else return d;}var Kc=[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509];var Lc=(1<<26)/Kc[Kc.length-1];function Mc(t){var i,x=this.abs();if(x.t==1&&x[0]<=Kc[Kc.length-1]){for(i=0;i>1;if(t>Kc.length)t=Kc.length;var a=ea();for(var i=0;i= 2","the exponent must be positive","the parameter of O() must be X^n","when composing two power series, the input must have no constant term","power serie with negative exponent forbidden here","integration would yield a log","cannot give a power expansion of log at this point"];function sd(a){var v;v=new Object();v.type=Pc;v.val=a;return v;}function td(a){return sd(new da(a+"",10));}var ud=sd(da.ZERO);var vd=sd(da.ONE);var wd=td(-1);var xd=new Array(0);var yd=COUT_MODE_FRAC;var zd=new Array(0);var Ad=1.0;var Bd,Cd,Dd;function Ed(Fd){Dd=Fd;Fd--;if(Fd<0||Fd>=rd.length){Gd("unknown error",Bd,Cd);}else{Gd(rd[Fd],Bd,Cd);}}function Hd(Id){return(Id.type==Pc&&Id.val.compareTo(da.ONE)==0);}function Jd(Id){return(Id.type==Pc&&Id.val.compareTo(wd.val)==0);}function Kd(Ld,Md){return sd(new da(Ld,Md));}function Nd(Id,Md){return Id.val.toString(Md);}function Od(Id,Pd){return sd(Id.val.add(Pd.val));}function Qd(Id,Pd){return sd(Id.val.subtract(Pd.val));}function Rd(Id){return sd(Id.val.negate());}function Sd(Id){return sd(Id.val.abs());}function Td(Id,Pd){return sd(Id.val.multiply(Pd.val));}function Ud(Id,Pd){return sd(Id.val.divide(Pd.val));}function Vd(Id,Pd){var r,b;b=Pd.val;if(b.signum()>=0){if(Id.val.signum()>=0){r=Id.val.remainder(b);}else{r=Id.val.negate();r=r.remainder(b);if(r.signum()!=0){r=b.subtract(r);}}}else{b=b.negate();if(Id.val.signum()>=0){r=Id.val.remainder(b);if(r.signum()!=0){r=b.subtract(r);}}else{r=Id.val.negate();r=r.remainder(b);r=r.negate();}}return sd(r);}function Wd(Id,Pd){return sd(Id.val.pow(Pd.val));}function Xd(Id,Pd){if(Id.type!=Pc||Pd.type!=Pc)Ed(ad);return sd(Id.val.gcd(Pd.val));}function Yd(Id,Pd){if(Zd(Id)>=0){return Ud(Id,Pd);}else{return Rd(Ud(Qd(Od(Rd(Id),Pd),vd),Pd));}}function ae(n){var r,i,n;n=be(n);r=vd;for(i=2;i<=n;i++){r=ce(r,td(i));}return r;}function de(Id,Pd){if(Id.type!=Pc||Pd.type!=Pc)Ed(ad);if(Zd(Pd)==0)Ed(bd);if(Zd(Pd)<0)Ed(jd);if(Zd(Id)<0)Id=Vd(Id,Pd);return sd(Id.val.modInverse(Pd.val));}function ee(Id,Pd){var t;if(Id.type!=Pc)Ed(ad);t=30;if(arguments.length>=2){t=be(Pd);if(t<=1)t=1;}if(Id.val.isProbablePrime(t))return vd;else return ud;}function fe(Id){if(Id.type!=Pc)Ed(ad);for(;;){Id=Od(Id,vd);if(Id.val.isProbablePrime(30))break;}return Id;}function ge(Id,Pd,he){if(Pd.type!=Pc)Ed(ad);if(Id.type==Pc&&he.type==Pc){if(Zd(he)==0)Ed(bd);if(Zd(he)<0)Ed(jd);if(Zd(Pd)<0){Id=de(Id,he);Pd=Rd(Pd);}return sd(Id.val.modPow(Pd.val,he.val));}else if(Id.type==Tc&&he.type==Tc){return ie(Id,Pd,he);}else{Ed(ad);}}function je(Id){var r,ke,s,d,le,me;if(Id.type!=Pc)Ed(ad);if(ne(Id,vd)<=0)Ed(kd);r=oe(0);ke=r.tab;d=td(2);while(pe(Vd(Id,d))){ke[ke.length]=d;Id=Ud(Id,d);}d=td(3);me=td(2);while(!Hd(Id)){if(!pe(ee(Id))){ke[ke.length]=Id;break;}for(;;){if(pe(Vd(Id,d)))break;d=Od(d,me);}for(;;){ke[ke.length]=d;Id=Ud(Id,d);if(!pe(Vd(Id,d)))break;}}r.dims[0]=ke.length;return r;}function qe(re,se){var r;r=new Object();r.type=Qc;r.num=re;r.den=se;return r;}function te(re,se){var r,s,g;s=se.val.signum();if(s==0){Ed(bd);}else if(s<0){re=Rd(re);se=Rd(se);}g=Xd(re,se);if(g.val.compareTo(da.ONE)!=0){re=Ud(re,g);se=Ud(se,g);}if(se.val.compareTo(da.ONE)==0){return re;}else{return qe(re,se);}return r;}function ue(Id){if(Id.type==Qc){return Id;}else if(Id.type==Pc){return qe(Id,vd);}else{Ed(ad);}}function ve(Id,Pd){Id=ue(Id);Pd=ue(Pd);return te(we(ce(Id.num,Pd.den),ce(Pd.num,Id.den)),ce(Id.den,Pd.den));}function xe(Id,Pd){Id=ue(Id);Pd=ue(Pd);return te(ye(ce(Id.num,Pd.den),ce(Pd.num,Id.den)),ce(Id.den,Pd.den));}function ze(Id,Pd){Id=ue(Id);Pd=ue(Pd);return te(ce(Id.num,Pd.num),ce(Id.den,Pd.den));}function Ae(Id,Pd){Id=ue(Id);Pd=ue(Pd);return te(ce(Id.num,Pd.den),ce(Id.den,Pd.num));}function Be(Id){return qe(Rd(Id.num),Id.den);}function Ce(Id){return qe(Sd(Id.num),Id.den);}function De(d){r=new Object();r.type=Rc;r.val=d;return r;}function Ee(Id){if(Id.type==Rc){return Id;}else if(Id.type==Pc){return De(new Number(Nd(Id,10)).valueOf());}else if(Id.type==Qc){return De(new Number(Nd(Id.num,10)).valueOf()/new Number(Nd(Id.den,10)).valueOf());}else{Ed(ad);}}function Fe(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Id.val+Pd.val);}function Ge(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Id.val-Pd.val);}function He(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Id.val*Pd.val);}function Ie(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Id.val/Pd.val);}function Je(Id){return De(-Id.val);}function Ke(Id){if(Id.val>=0)return td(Math.floor(Id.val));else return td(-Math.floor(-Id.val));}function Le(Id){return td(Math.floor(Id.val));}function Me(Id){return td(Math.ceil(Id.val));}function Ne(Id){return td(Math.round(Id.val));}function Oe(Id){var Ld;Ld=Id.val.toString();if(Ld.indexOf(".")<0&&Ld.indexOf("e")<0&&Ld.indexOf("NaN")<0&&Ld.indexOf("Inf")<0){Ld+=".0";}return Ld;}function Pe(Id){return De(Math.abs(Id.val));}function Qe(Id){Id=Ee(Id);return De(Math.sqrt(Id.val));}function Re(Id){Id=Ee(Id);return De(Math.exp(Id.val));}function Se(Id){Id=Ee(Id);return De(Math.log(Id.val));}function Te(Id){Id=Ee(Id);return De(Math.log(Id.val)/Math.LN2);}function Ue(Id){Id=Ee(Id);return De(Math.log(Id.val)/Math.LN10);}function Ve(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Math.pow(Id.val,Pd.val));}function We(Id){Id=Ee(Id);return De(Math.sin(Id.val*Ad));}function Xe(Id){Id=Ee(Id);return De(Math.cos(Id.val*Ad));}function Ye(Id){Id=Ee(Id);return De(Math.tan(Id.val*Ad));}function Ze(Id){Id=Ee(Id);return De(Math.asin(Id.val)/Ad);}function af(Id){Id=Ee(Id);return De(Math.acos(Id.val)/Ad);}function bf(Id){Id=Ee(Id);return De(Math.atan(Id.val)/Ad);}function cf(Id,Pd){Id=Ee(Id);Pd=Ee(Pd);return De(Math.atan2(Id.val,Pd.val));}function df(){return De(Math.PI);}function ef(Id){var x;Id=Ee(Id);x=Id.val;if(x==0){x=1;}else{x=Math.PI*x;x=Math.sin(x)/x;}return De(x);}var ff=gf(ud,vd);function gf(hf,jf){r=new Object();r.type=Sc;r.re=hf;r.im=jf;return r;}function kf(hf,jf){if(pe(jf)){return hf;}else{return gf(hf,jf);}}function lf(Id){if(Id.type==Sc)return Id;else return gf(Id,ud);}function mf(Id,nf){if(Id.type==Wc){return of(Id,nf);}else if(Id.type==Tc){return pf(Id,nf);}else if(Id.type==Vc){return qf(Id,nf);}else if(Id.type==Sc){return gf(nf(Id.re),nf(Id.im));}else{Ed(ad);}}function rf(Id){if(Id.type<=Rc){return Id;}else if(Id.type==Sc){return Id.re;}else{return mf(Id,rf);}}function sf(Id){if(Id.type<=Rc){return ud;}else if(Id.type==Sc){return Id.im;}else{return mf(Id,sf);}}function tf(Id){var s;if(Id.type<=Rc){s=Zd(Id);if(s==0)Ed(cd);if(s<0)return df();else return ud;}else if(Id.type==Sc){return cf(Id.im,Id.re);}else{return mf(Id,tf);}}function uf(Id,Pd){Id=lf(Id);Pd=lf(Pd);return kf(we(Id.re,Pd.re),we(Id.im,Pd.im));}function vf(Id,Pd){Id=lf(Id);Pd=lf(Pd);return kf(ye(Id.re,Pd.re),ye(Id.im,Pd.im));}function wf(Id,Pd){Id=lf(Id);Pd=lf(Pd);return kf(ye(ce(Id.re,Pd.re),ce(Id.im,Pd.im)),we(ce(Id.re,Pd.im),ce(Id.im,Pd.re)));}function xf(Id){Id=lf(Id);return kf(yf(Id.re),yf(Id.im));}function zf(Id){Id=lf(Id);return kf(Id.re,yf(Id.im));}function Af(Id){Id=lf(Id);return we(ce(Id.re,Id.re),ce(Id.im,Id.im));}function Bf(Id){var c;Id=lf(Id);c=Af(Id);return gf(Cf(Id.re,c),yf(Cf(Id.im,c)));}function Df(Id,Pd){return wf(Id,Bf(Pd));}function Ef(Id){return Ff(Af(Id));}function Gf(Id){var Hf,r;Hf=Ee(Id.im);r=Re(Ee(Id.re));return gf(He(Xe(Hf),r),He(We(Hf),r));}function If(Id){var Hf,r;Id=lf(Id);Hf=cf(Ee(Id.im),Ee(Id.re));r=Ee(Ef(Id));return gf(Se(r),Hf);}function Jf(Id,Pd){return Gf(wf(If(Id),Pd));}function be(Id){if(typeof(Id)=="number"){return Id;}else if(Id.type==Pc){return Id.val.intValue();}else{Ed(ad);}}function oe(n){var n;r=new Object();r.type=Wc;r.dims=new Array(1);r.dims[0]=n;r.tab=new Array(n);for(i=0;i2)Ed(gd);l=Id.dims[1];if(l!=Pd.dims[0])Ed(gd);r=new Object();r.type=Wc;h=Id.dims[0];r.dims=new Array(Pd.dims.length);if(Pd.dims.length==2){w=Pd.dims[1];r.dims[0]=h;r.dims[1]=w;}else{w=1;r.dims[0]=h;}ke=new Array(w*h);r.tab=ke;jg=Id.tab;kg=Pd.tab;for(i=0;i1&&pe(Id.tab[i-1]))i--;if(i==n)return Id;r=Tf(i);for(j=0;j0){n--;v=we(ce(v,Pd),ke[n]);}return v;}function Lg(Id){var ke,n,i,p;ke=Id.tab;n=ke.length;if(n==1){p=Tf(1);p.tab[0]=ud;}else{p=Tf(n-1);for(i=1;i=0)n-=Ng(Id.den);}else{Ed(ad);}return td(n);}function Pg(Id,Pd,Qg){var jg,kg,Gg,Oc,og,i,j,q;Gg=Id.tab;Oc=Gg.length;kg=Pd.tab;og=kg.length;if(Oc=0;i--){c=jg[i+og-1];if(!pe(c)){c=Cf(c,kg[og-1]);for(j=0;j=0){Gg=Pd;Pd=Tg(Id,Pd);Id=Gg;}Id=Cf(Id,Id.tab[Id.tab.length-1]);return Id;}function Ug(Id){var i,Ld,Vg,c;Ld="";for(i=Id.tab.length-1;i>=0;i--){c=Id.tab[i];if(!pe(c)||(i==0&&Id.tab.length==1)){if(i==0){Vg=zg(c);}else{if(Hd(c)){Vg="";}else if(Jd(c)){Vg="-";}else{Vg=zg(c)+"*";}Vg+="X";if(i>=2){Vg+="^"+i;}}if(Vg.charAt(0)!="-"){if(Ld!="")Ld+="+";}Ld+=Vg;}}return Ld;}function Wg(p,z,Xg,Yg){var Zg,ah,i,bh,ch,dh,d,eh,fh,ab,bb;d=Ng(p);if(d==1){return yf(Cf(p.tab[0],p.tab[1]));}Xg=gh(Xg);Zg=Lg(p);ah=Lg(Zg);for(i=0;i0)ab=bb;if(pe(ab))return null;z=ye(z,Cf(ce(td(d),bh),ab));}return null;}function Vf(p){var d,i,hh,ih,j;var jh=[0.1,-1.4,1.7];if(p.type!=Tc)Ed(ad);d=Ng(p);if(d==-1){Ed(hd);}hh=oe(d);for(i=0;i0){re=Rg(re,g);se=Rg(se,g);}if(Ng(se)==0){return Cf(re,se.tab[0]);}else{return kh(re,se);}return r;}function mh(Id){var Pd;if(Id.type==Uc){return Id;}else{Pd=Tf(1);Pd.tab[0]=vd;return kh(Eg(Id),Pd);}}function nh(Id,Pd){Id=mh(Id);Pd=mh(Pd);return lh(we(ce(Id.num,Pd.den),ce(Pd.num,Id.den)),ce(Id.den,Pd.den));}function oh(Id,Pd){Id=mh(Id);Pd=mh(Pd);return lh(ye(ce(Id.num,Pd.den),ce(Pd.num,Id.den)),ce(Id.den,Pd.den));}function ph(Id,Pd){Id=mh(Id);Pd=mh(Pd);return lh(ce(Id.num,Pd.num),ce(Id.den,Pd.den));}function qh(Id,Pd){Id=mh(Id);Pd=mh(Pd);return lh(ce(Id.num,Pd.den),ce(Id.den,Pd.num));}function rh(Id){return kh(yf(Id.num),Id.den);}function sh(n,th){var r,i;r=new Object();r.type=Vc;r.tab=new Array(n);r.e_min=th;for(i=0;i=0&&j=0&&j0){n--;v=we(ce(v,Pd),ke[n]);}if(Id.e_min!=0){v=ce(v,Jh(Pd,td(Id.e_min)));}if(Pd.type==Tc||Pd.type==Uc){v=yh(v,Id.tab.length*th);}}else{if(Pd.type==Vc)return Id;else return ud;}return v;}function Kh(Id){var n,i,j,r;n=Id.tab.length;if(n==0){if(Id.e_min==0)return sh(0,0);else return sh(0,Id.e_min-1);}else{r=sh(n,Id.e_min-1);for(i=0;i0){c=vd;}else{if(Id.tab.length==0)return Id;c=Oh(Id.tab[0]);Id=Mh(Id);}n=Math.ceil((Id.e_min+Id.tab.length)/Id.e_min);r=sh(n,0);for(i=0;i0)return 1;else if(Id.val==0)return 0;else return-1;}}function pe(Id){return(Zd(Id)==0);}function ne(Id,Pd){return Zd(ye(Id,Pd));}function we(Id,Pd){Xh=Math.max(Id.type,Pd.type);if(Xh==Pc){return Od(Id,Pd);}else if(Xh==Qc){return ve(Id,Pd);}else if(Xh==Rc){return Fe(Id,Pd);}else if(Xh==Sc){return uf(Id,Pd);}else if(Xh==Tc){return Fg(Id,Pd);}else if(Xh==Uc){return nh(Id,Pd);}else if(Xh==Vc){return Bh(Id,Pd);}else if(Id.type==Wc&&Pd.type==Wc){return gg(Id,Pd,we);}else{Ed(ad);}}function ye(Id,Pd){var Xh;Xh=Math.max(Id.type,Pd.type);if(Xh==Pc){return Qd(Id,Pd);}else if(Xh==Qc){return xe(Id,Pd);}else if(Xh==Rc){return Ge(Id,Pd);}else if(Xh==Sc){return vf(Id,Pd);}else if(Xh==Tc){return Hg(Id,Pd);}else if(Xh==Uc){return oh(Id,Pd);}else if(Xh==Vc){return Eh(Id,Pd);}else if(Id.type==Wc&&Pd.type==Wc){return gg(Id,Pd,ye);}else{Ed(ad);}}function ce(Id,Pd){var Xh;Xh=Math.max(Id.type,Pd.type);if(Xh==Pc){return Td(Id,Pd);}else if(Xh==Qc){return ze(Id,Pd);}else if(Xh==Rc){return He(Id,Pd);}else if(Xh==Sc){return wf(Id,Pd);}else if(Xh==Tc){return Jg(Id,Pd);}else if(Xh==Uc){return ph(Id,Pd);}else if(Xh==Vc){return Fh(Id,Pd);}else if(Id.type==Wc&&Pd.type<=Sc){function Yh(c){return ce(c,Pd);}return of(Id,Yh);}else if(Pd.type==Wc&&Id.type<=Sc){function Yh(c){return ce(c,Id);}return of(Pd,Yh);}else if(Id.type==Wc&&Pd.type==Wc){return hg(Id,Pd);}else{Ed(ad);}}function Cf(Id,Pd){var Xh;Xh=Math.max(Id.type,Pd.type);if(Xh==Pc){return te(Id,Pd);}else if(Xh==Qc){return Ae(Id,Pd);}else if(Xh==Rc){return Ie(Id,Pd);}else if(Xh==Sc){return Df(Id,Pd);}else if(Id.type==Tc&&Pd.type<=Sc){function Zh(c){return Cf(c,Pd);}return pf(Id,Zh);}else if(Xh==Tc){return lh(Eg(Id),Eg(Pd));}else if(Xh==Uc){return qh(Id,Pd);}else if(Xh==Vc){return Hh(Id,Pd);}else if(Id.type==Wc&&Pd.type<=Sc){function Zh(c){return Cf(c,Pd);}return of(Id,Zh);}else if(Id.type==Wc&&Pd.type==Wc){return hg(Id,rg(Pd));}else{Ed(ad);}}function Tg(Id,Pd){var Xh;Xh=Math.max(Id.type,Pd.type);if(Xh==Pc){return Vd(Id,Pd);}else if(Xh==Qc||Xh==Rc){return ye(Id,ce(Pd,ai(Cf(Id,Pd))));}else if(Id.type==Wc&&Pd.type<=Rc){function bi(c){return Tg(c,Pd);}return of(Id,bi);}else if(Id.type==Tc&&Pd.type<=Rc){function bi(c){return Tg(c,Pd);}return pf(Id,bi);}else if(Id.type==Tc&&Pd.type==Tc){return Pg(Id,Pd,true);}else{Ed(ad);}}function zg(Id){var Ld,Vg;if(Id.type==Pc){if(yd==COUT_MODE_HEXA){if(Id.val.signum()<0){Ld="-";Id=Rd(Id);}else{Ld="";}Ld+="0x"+Nd(Id,16);}else{Ld=Nd(Id,10);}}else if(Id.type==Qc){if(yd==COUT_MODE_REAL){Ld=Oe(Ee(Id));}else{Ld=zg(Id.num);Ld+="/"+zg(Id.den);}}else if(Id.type==Rc){Ld=Oe(Id);}else if(Id.type==Sc){if(pe(Id.re)){Ld="";}else{Ld=zg(Id.re);}if(Hd(Id.im)){if(Ld!="")Ld+="+";Ld+="I";}else if(Jd(Id.im)){Ld+="-I";}else{Vg=zg(Id.im);if(Vg.charAt(0)!="-"){if(Ld!="")Ld+="+";}Ld+=Vg+"*I";}}else if(Id.type==Wc){Ld=Ag(Id);}else if(Id.type==Xc){Ld="[function]";}else if(Id.type==Tc){Ld=Ug(Id);}else if(Id.type==Uc){Ld="("+zg(Id.num)+")";Ld+="/("+zg(Id.den)+")";}else if(Id.type==Vc){Ld=uh(Id);}else if(Id.type==Yc){Ld=Uh(Id);}else{Ld="[cannot display this object]";}return Ld;}function ci(Id,Pd){var e,r,s;if(Id.type==Wc){r=Lf(Qf(Id));}else if(Id.type==Tc||Id.type==Uc){r=Cg();}else{r=vd;}e=Pd.val;s=e.signum();if(s!=0){if(s<0){Id=qg(Id);e=e.negate();}for(;;){if(!e.isEven()){r=ce(r,Id);}e=e.shiftRight(1);if(e.signum()==0)break;Id=ce(Id,Id);}}return r;}function Jh(Id,Pd){if(Pd.type==Pc){return ci(Id,Pd);}else if(Id.type<=Rc&&Pd.type<=Rc){return Ve(Id,Pd);}else if(Id.type<=Sc&&Pd.type<=Sc){return Jf(Id,Pd);}else if(Id.type==Vc||Pd.type==Vc){return Nh(ce(Ph(Id),Pd));}else{Ed(ad);}}function di(Id,Pd){if(Id.type==Pc&&Id.type==Pc){return Xd(Id,Pd);}else if(Id.type==Tc&&Id.type==Tc){return Sg(Id,Pd);}else{Ed(ad);}}function Oh(Id){if(Id.type<=Rc){return Re(Id);}else if(Id.type==Sc){return Gf(Id);}else if(Id.type==Vc){return 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';for(i=0;i<(Ii-Hi);i++){Ld+='

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';Ld+='

';Ld+='

';Ld+='

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'+Nl[i].cmd;Ld+='

'+Nl[i].line+'

";}Kl.innerHTML=Ld;}function Rl(){var Kl,i,j,cat,Ld,e;Kl=document.getElementById("help_output");Ld="";Ld+='Here are the units known by the calculator.
';Ld+='Example: convert(32, "inches", "cm") to convert 32 inches to centimeters.';Ld+='';Ld+='';for(j=0;j';}Ld+='

Name	Abbrev	Value
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'+e.name+'	'+e.abbrev+'	'+e.val+' '+e.unit;if(e.addend){Ld+=' (offset '+e.addend+')';}Ld+='

';Ld+='

Unit prefixes:';Ld+='';Ld+='';for(j=0;j
Prefix name Abbrev Value
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';Kl.innerHTML=Ld;}function change_help_tab(name){var bk,Kl;adjustFocus();if(ol==name)return;if(ol){bk=document.getElementById("but_"+ol);bk.style.backgroundColor="rgb(210,210,255)";}bk=document.getElementById("but_"+name);bk.style.backgroundColor="rgb(230,230,255)";ol=name;Jl();if(name=="contextual"){contextual_help_show();}else if(name=="tutorial"){Kl=document.getElementById("help_output");Kl.innerHTML=Sl;}else if(name=="reference"){Pl();}else if(name=="units"){Rl();}else if(name=="faq"){Kl=document.getElementById("help_output");Kl.innerHTML=Tl;}}function change_tab(name){var bk;adjustFocus();if(name==Ok)return;if(Ok){bk=document.getElementById("but_"+Ok);bk.style.backgroundColor="rgb(210,210,255)";}bk=document.getElementById("but_"+name);bk.style.backgroundColor="rgb(230,230,255)";if(Ok){if(Ok=="results"){bk=document.getElementById("calc_output");}else if(Ok=="plot"){bk=document.getElementById("plot_tab");}else if(Ok=="variables"){bk=document.getElementById("var_list");}bk.style.display="none";}if(name=="results"){bk=document.getElementById("calc_output");}else if(name=="plot"){bk=document.getElementById("plot_tab");}else if(name=="variables"){bk=document.getElementById("var_list");}bk.style.display="block";if(name=="results"){ul();ul();}else if(name=="plot"){Ik(true);}else if(name=="variables"){Cj();}Ok=name;}function calc_init(){var bk;document.getElementById("output_mode_frac").checked=(yd==COUT_MODE_FRAC);document.getElementById("output_mode_real").checked=(yd==COUT_MODE_REAL);document.getElementById("output_mode_hexa").checked=(yd==COUT_MODE_HEXA);document.getElementById("angle_mode_rad").checked=true;document.getElementById("angle_mode_deg").checked=false;bj();jl=wl("charw");bk=document.getElementById("calc_output");kl=Math.floor((bk.clientWidth-24)/wl("ocharw"));gk();adjustFocus();change_tab("results");change_help_tab("contextual");Cj();bk=document.getElementById("calc_input");bk.value=Ml;bk.select();}var Ml="Type your formula here";var Ql=[{cat:"arith",name:"Arithmetic"},{cat:"bit",name:"Bit Manipulation"},{cat:"trans",name:"Transcendental"},{cat:"linear",name:"Linear Algebra, Matrixes"},{cat:"poly",name:"Polynomial, Power series"},{cat:"plot",name:"Plot and Equation solving"},{cat:"misc",name:"Miscellaneous"}];var Nl=[{name:"inverse",cat:"arith",cmd:"inverse(x)",line:"Inverse of x"},{name:"norm",cat:"arith",cmd:"norm(x)",line:"Norm of x. For a real number, return x^2. For a complex number, return re(x)^2+im(x)^2"},{name:"abs",cat:"arith",cmd:"abs(x)",line:"Absolute value of x. For a complex number, return sqrt(re(x)^2+im(x)^2)"},{name:"trunc",cat:"arith",cmd:"trunc(x)",line:"Largest integer in absolute value <= x. If x is a rational fonction, return its integer part."},{name:"floor",cat:"arith",cmd:"floor(x)",line:"Largest integer <= x"},{name:"ceil",cat:"arith",cmd:"ceil(x)",line:"Smallest integer >= x"},{name:"round",cat:"arith",cmd:"round(x)",line:"Closest integer to x. If halfway, takes the largest integer."},{name:"num",cat:"arith",cmd:"num(x)",line:"Return the numerator of the fraction x."},{name:"den",cat:"arith",cmd:"den(x)",line:"Return the denominator of the fraction x."},{name:"fact",cat:"arith",cmd:"fact(n)",line:"Factorial of n"},{name:"frac",cat:"arith",cmd:"frac(x[,e])",line:"Fractional approximation of x. The optional parameter e gives the precision."},{name:"bin",cat:"bit",cmd:"bin(n)",line:"Convert n to binary"},{name:"hex",cat:"bit",cmd:"hex(n)",line:"Convert n to hexadecimal"},{name:"xor",cat:"bit",cmd:"xor(a,b)",line:"Bitwise exclusive or between the integers a and b"},{name:"sqrt",cat:"arith",cmd:"sqrt(x)",line:"Square root of x"},{name:"conj",cat:"arith",cmd:"conj(x)",line:"Complex conjugate of x"},{name:"re",cat:"arith",cmd:"re(x)",line:"Real part of the complex number x"},{name:"im",cat:"arith",cmd:"im(x)",line:"Imaginary part of the complex number x"},{name:"arg",cat:"arith",cmd:"arg(x)",line:"Argument of the complex number x (-PI<arg(x)<=PI)"},{name:"gcd",cat:"arith",cmd:"gcd(a,b)",line:"Greatest Common Divisor of a and b (integers or polynomials)"},{name:"isprime",cat:"arith",cmd:"isprime(n[,t])",line:"Return 1 if n is prime, 0 if not. A probabilistic Miller Rabin test is done. If 1 is returned, the probability that n is not prime is 1-0.5^t. 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Return -(2^31 - 1) if p is the zero polynomial"},{name:"apply",cat:"poly",cmd:"apply(p, a)",line:"Evaluate the the polynomial, rational fonction or power series p by replacing the variable with a"},{name:"deriv",cat:"poly",cmd:"deriv(p)",line:"Derivative of the polynomial, rational fonction or power series p"},{name:"integ",cat:"poly",cmd:"integ(p)",line:"Formal integration of the polynomial or power series p. The constant term is set to zero"},{name:"polroots",cat:"poly",cmd:"polroots(p)",line:"Return a vector containing the roots of polynomial p."},{name:"plot",cat:"plot",cmd:"plot(var, func[,xmin]
[,xmax][,ymin][,ymax])",line:'Plot the function func. var is a string defining the variable. Example: plot("x", "sin(x)", -2, 2)'},{name:"solve",cat:"plot",cmd:"solve(var, f, x0)",line:'Find an approximation of the solution of f(var) = 0. x0 is the initial guess. Example: solve("x", "x^2-2", 1.5)'},{name:"convert",cat:"misc",cmd:"convert(x,unit1,unit2)",line:'Convert the quantity x expressed in unit1 to unit2. Example: convert(32, "inches", "cm") to convert 32 inches to centimeters. Unit names and abbreviations are known. All prefixes (e.g. kilo) are supported. The unit converter knowns about dimensions: convert(1, "km/h", "m/s") or convert(1, "km^2", "ft^2").'},{name:"clear",cat:"misc",cmd:"clear()",line:"Clear the history"},{name:"typeof",cat:"misc",cmd:"typeof(x)",line:"Return a string identifying the type of x"},{name:"X",cat:"poly",cmd:"X",line:"Return the degree one polynomial 'X'"},{name:"I",cat:"arith",cmd:"I",line:"Square root of -1"},{name:"PI",cat:"trans",cmd:"PI",line:"Pi constant"},{name:"+",cat:"arith",cmd:"a+b",line:"Add two numbers, polynomials or matrixes"},{name:"-",cat:"arith",cmd:"a-b",line:"Substract two numbers, polynomials or matrixes"},{name:"*",cat:"arith",cmd:"a*b",line:"Multiply two numbers, polynomials or matrixes"},{name:"/",cat:"arith",cmd:"a/b",line:"Divide two numbers, polynomials or matrixes"},{name:"%",cat:"arith",cmd:"a%b",line:"Euclidian remainder of a divided by b, defined as 'a - floor(a/b) * b'"},{name:"&",cat:"bit",cmd:"a&b",line:"Bitwise and between the integers a and b"},{name:"|",cat:"bit",cmd:"a|b",line:"Bitwise or between the integers a and b"},{name:"~",cat:"bit",cmd:"~n",line:"Bitwise not of the integer n"},{name:"^",cat:"arith",cmd:"a^b",line:"a raised to the power of y"},{name:"<<",cat:"bit",cmd:"a<<n",line:"Shift left by n bits. Equivalent to a*2^n"},{name:">>",cat:"bit",cmd:"a>>n",line:"Shift right by n bits. Equivalent to floor(a/2^n)"},{name:"[",cat:"linear",cmd:"[1,2,3]",line:"Enter a vector"},{name:"[",cat:"linear",cmd:"[[1,2][3,4]]",line:"Enter a matrix"},{name:"[",cat:"linear",cmd:"[",line:"x[n] is the nth element of vector x. x[n,m] is the matrix element on row n and colomn m. x[n1:n2] is the sub vector of x whose element indexes i are such as n1<=i<n2. x[n1:n2,m1:m2] similarily defines a sub matrix. x[n,m1:m2] (resp. x[n1:n2,m] extract a matrix row (resp. column)."},{name:"%",cat:"misc",cmd:"%{n}",line:"% recalls the last result. %n recalls a previous result identified by n."}];var Ol="Examples:"+""+''+''+''+''+''+''+''+''+''+''+''+''+"
1/3+1/2 Exact results are given when dealing with fractions
1.0/3 The calculator falls back to floating point numbers when it cannot give an exact result or when you request it explicitely by using a decimal point
plot("x","sin(x)") Plot the sin(x) function
convert(2,"ft^2",
"m^2") Convert 2 square feet to square meters
a=1 Create a new variable "a"
% Reuse last result (%n selects the nth result). Use the arrow keys {Up} and {Down} to reuse your last inputs.
0x1a Hexadecimal number
(1+2*I)^2 Use "I" to enter complex numbers
[1,2,3]*3 vector operators
det([[1,2][3, 4]]) determinant of a 2x2 matrix
(1+X)^5 Use "X" to manipulate polynomials
sin(X+O(X^6)) Taylor expansion at order 5 of sin(x)
";var Sl='NumCalc is a lightweight and easy to use scientific web calculator. It has the following features:'+'

Arbitrary precision integers and fractions'+'
Graphical plot of arbitrary functions'+'
Numerical equation solving'+'
Unit conversions'+'
All computations are made locally in your browser. Your privacy is kept because no data is sent back to our servers.'+'

'+"The more mathematically inclined users will also enjoy the following features:"+'

Complex numbers including complex transcendental functions'+'
Polynomials, rational fonctions and Taylor series'+'
Linear algebra: matrix inversion, rank, eigen values and kernel extraction.'+'

'+'

Basic Use

'+'You can type:'+'

2*(1+3)

'+'which yields:'+'

%1 = 8

'+'Then'+'

3*%1

'+'which yields:'+'

%2 = 24

'+'%1 indicates that you reuse the first result. % alone is the last result.'+'

Fractions: unlike other calculators, NumCalc tries to give exact results with fractions:'+'

1/3+1/2

'+'which yields:'+'

%1 = 5/6

'+'You can still get the approximative floating point result either by changing the output format (Real button on top) or by using a decimal point in your input:'+'

1/3+1/2.0

'+'which yields:'+'

%1 = 0.8333333333333333

'+'

Precision: fractions and integers are not limited in size (except by the memory of your PC and the time you want to spent waiting for the result !). For example:'+'

2^256

'+'yields the exact value of 2 to the power of 256.'+'

Functions: all the usual mathematical functions are available such as: sqrt (square root), sin, cos, tab, log (logarithm in base e), exp, ...
Constants are referenced by upper case names, e.g. PI for the pi constant. Example:'+'

sin(PI/8)

'+'

%1 = 0.3826834323650898

'+'

Variables: You can store your results in variables and reuse them in the following expressions:'+'

a=sin(PI/8)

'+'

b=sqrt(a)

'+'

Multiple expressions: You can type several expressions on the same line by separating them with a ;. If the line ends with a ;, the result is not printed:'+'

a=1+3;b=a^2+1;

'+'

Graphical plots: expressions can easily be plotted:'+'

plot("x", "sin(x)")

'+'You can specify the x range with additional parameters:'+'

plot("x", "sin(x)/x",-2*PI,2*PI)

'+'The y range is found automatically, but you can also specify it:'+'

plot("x", "sin(x)/x",-2*PI,2*PI,-1,1)

'+'

Equation solving: NumCalc can find a numerical solution for single variable equations. Let say you want to solve cos(x)=x. You can plot the function cos(x)-x to have an idea of the position of the solution:'+'

plot("x", "cos(x)-x")

'+'Then you can feed the calculator with the initial guess (say 0.8) to have a more precise solution:'+'

solve("x", "cos(x)-x", 0.8)

'+'

%1 = 0.7390851332151606

'+"

Unit convertion: the calculator can convert between most physical units. It also knows how to combine units and tell whether they measure the same quantity (i.e. it does dimensional analysis).
You can specify units either by typing their full name (e.g. kilometers or by using the standar abbreviation (e.g. km). Units can be combined with *, ^ and / (e.g. km*h^-1 or km/h are the same).
Example of unit conversions. Let's say you want to convert 10 meters per second to kilometers per hour:"+'

convert(10, "m/s", "km/h")

'+'

%1=36.0

'+'All the understood units and prefixes can be access in the online help.'+'

Binary arithmetic: Use the 0x prefix to enter hexadecimal numbers (e.g. 0x1a). The 0b prefix is used for binary numbers. You can change the output format to print hexadecimal integers (button Hexa on top).
'+'The calculator supports all standard bitwise logical and shift operators with a C like syntax. The notable exception is the exclusive or which is implemented with the xor(x,y) function because the ^ binary operator is reserved for powers.
'+"All binary arithmetic functions assume that integers are represented in two's complement notation. Hence a negative number can be seen as having an infinite number of '1' to the left.
"+'

Advanced Use

'+"You can stop reading this tutorial at this point if you don't intend to deal with more advanced mathematical objects
"+'

Complex numbers: use the constant I to enter complex numbers:'+'

(1+2*I)*(2+3*I)

'+'Most predefined functions deal with complex numbers:'+'

exp(-I*PI)

'+'

Polynomials: use the constant X to enter polynomials. Polynomials are represented internally as an array of their coefficient, so the actual variable used to represent them does not matter. In the calculator, the X variable is used by convention.'+'

(1+X)^3

'+'

%1 = X^3+3*X^2+3*X+1

'+'You can evaluate a polynomial at one point by using the apply function:'+'

p=(1+X)^3;apply(p, 1/2)

'+'apply is also useful to substitute the X variable with another polynomial.
'+"A polynomial complex root finder based on the Laguerre's method is also included:"+'

polroots(X^3-1)

'+'

Rational fonctions: if you divide two polynomials you get a rational fonction and they can be manipulated as objects too:'+'

deriv(1/(1+X)+2/(2+X)+3/(3+X))

'+'gets the derivative of the rational function. Note that integration of rational fonctions is not supported.'+'

Taylor series: Taylor series are created with the O function. Taylor series can be seen as polynomials where all the terms of degrees >= O(X^n) are thrown again. To be more precise, the calculators handles Laurent series as well. It means that the exponents can be negative too.
Example of use:'+'

(1+X+O(X^3))^(1/3)

'+'

%1 = 1+1/3*X-1/9*X^2+O(X^3)

'+'Computes the order 2 taylor expansion of (1+x)^(1/3). The calculator also knows the Taylor expansion of most usual functions:'+'

sin(X+O(X^4))

'+'

%2 = X-1/6*X^3+O(X^4)

'+'

Linear algebra: Vectors and matrixes are supported. Example:
'+'Enter a 3x3 matrix:'+'

a=[[1,2,3][2,3,4][5,6,8]]

'+'Compute its determinant:'+'

det(a)

'+'Inverse it:'+'

inverse(a)

'+'Sub matrixes can be extracted and assigned to (same idea as the Python language):'+'

a[1:3,1:3]

'+'

%1 = [[3, 4][6, 8]]

'+'Extracts the 2x2 bottom left sub matrix of a.
'+'The functions rank, ker, charpoly and eigenvals yield respectively the rank, kernel, characteric polynomial and eigen values of a matrix.
'+'Vectors are also supported:'+'

v=[1,2,3]

'+'When dealing with matrix multiplication, they are considered as column vectors, e.g:'+'

a*v

'+'

%2 = [14, 20, 41]

'+'dp(x,y) does the dot product of vectors. cp(x,y) does the 3 dimensional cross product of vectors. Most operations defined on numbers also work on vectors and matrixes component-wise.'+'

Primes: isprime(n) and testprime(n) test if a number is prime using the Miller Rabin probabilistic test. factor(n) factorize a number using trial divisions.'+'

Modulo arithmetic: although the calculator does not handle modulo N numbers as objects, it has some functions to help working with them: invmod(a,m) returns the inverse of a modulo m. pmod(a,b,m) compute a^b modulo m with less computational resources than doing a^b%m. It also works with polynomials.
'+'The fact that the modulo binary operator (%) applies component wise on polynomials can be used to make computation with polynomials whose coefficients are in Z/nZ, which helps in turns to make computations in Galois fields:'+'

((1+X+X^3)*(1+X^3)%(1+X+X^4))%2

'+'

%1 = X^3+X^2

'+'Computes the product of two polynomials modulo (1+X+X^4) whose coeficients are in F₂'+'

Credits

'+'NumCalc borrows many ideas from PARI/GP, calc and the old HP48 calculator. NumCalc uses the jsbn library written by Tom Wu.'+'';var Tl='

Are my computations sent to a server ?

'+'

No. All computations are made locally in your browser. Hence NumCalc preserves your privacy.

'+'

Why aren\'t they buttons for all functions as in other PC calculators ?

'+'

Having buttons on screen is not useful as you already have ones on the keyboard ! We believe it is much faster and easier to enter calculus using the standard PC keys.

'+'

How can I reuse my previous inputs or results ?

'+'

With the {Up} and {Down} arrow keys you get your last inputs. With the % symbol, you get the previous result. With %N, you get the result number N.

'+'

How can I get a floating point (= real) result ?

'+'

NumCalc always tries to give an exact result, so it is normally a fraction. You can use the Output Format "Real" button to indicate that you wish to display fractions as real numbers (internally the result is still a fraction). If you wish to convert a fraction to a floating point result, you can add 0.0 to it: 1/3+0.0 .

'+'

Can I make symbolic calculus with NumCalc ?

'+'

NumCalc is not a generic symbolic calculator: it cannot simplify mathematical expressions. However, it does arbitrary precision computations involving integers, fractions, complex numbers, polynomial and matrixes, which are suffisent for many mathematical and engineering tasks.

'+'

How can I enter a polynomial ?

'+'

You must use the X variable. Try for example (1+X)^10 . Polynomials are stored internally as array of coefficients. The fact that they are displayed as conventional expressions is a cosmetic feature.

'+'

How can I convert between units ?

'+'

Use the convert function. Example: convert(32, "inches", "cm") .

'+'

How can I get the Taylor expansion of a function ?

'+'

O(x^n) indicates that you are manipulating Taylor series. Example: sin(X+O(X^10)) to get the Taylor expansion of sin(x) at order 9.

'+'

Can I get the derivative or integral of a function ?

'+'

NumCalc is not a symbolic calculator, so it cannot give you the result for arbitrary functions. However, as it manipulates polynomials, rational fonctions and power series, it can give the answer for them. Example: deriv((1+X^2)/(2+X)), integ(1+X^2)

'+'

I cannot see plots. What\'s wrong ?

'+'

Your browser must support the Javascript Canvas. Most recent browsers support them. We made test with Firefox 1.5 and 2.0 and MSIE 6.0

'+"";