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added differential operator, so now you can graph a derivative by mul…
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…tiplying d/dx by somthing, or by d*f(x)/dx
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Anthony committed Jan 5, 2011
1 parent 9a3c359 commit 5edeb81
Showing 1 changed file with 187 additions and 30 deletions.
217 changes: 187 additions & 30 deletions math.js
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Original file line number Diff line number Diff line change
Expand Up @@ -217,6 +217,12 @@ function Gamma(x) {
return pow(x - 1, x - 1) * Math.sqrt(2 * Math.PI * (x - 1)) * exp(1 - x + 1 / (12 * (x - 1) + 2 / (5 * (x - 1) + 53 / (42 * (x - 1)))));
}
}

function psi(x) {
return random();
}
Γ=Gamma;
ψ=psi;
function fact(ff) {
if (ff === 0 || ff == 1) {
return 1;
Expand Down Expand Up @@ -365,8 +371,8 @@ function __debug(x){
var spaces=" ";
var level=0;
function p(inp){
if(typeof inp=="number"){
return Num(inp);
if(typeof inp=="number" || !isNaN(inp)){
return Number(inp);
}else if(typeof inp=="object"){
return inp;
}
Expand All @@ -375,16 +381,15 @@ function p(inp){
}
//parses brackets recursively and returns an expression

level++;
if(level>15){throw("too recursive for debugging");return;}
//level++;
//if(level>15){throw("too recursive for debugging");return;}
__debug(!__debug_parser,0) || console.log(spaces.substring(0,level)+"p: "+inp);
var eq=[];
var e=inp.replace(/\s/g,"").replace(/\]/g,")").replace(/\[/g,"(").replace(/\)\(/g,")*(");

//TODO: known functions only, otherwise make it a product
//TODO: allow things like 2x
e=e.replace(/([a-zA-Z])\(/g,"$1:(");

e=e.replace(/([^\+\-\*\/\^\:\(\)])\(/g,"$1:(");
if(e.indexOf("=")!=-1){
var eq=e.replace("==","[equals][equals]").split("=").map(function(e){return e.replace("[equals][equals]","==");});
if(eq.length==2){
Expand All @@ -396,7 +401,7 @@ function p(inp){
//---Recursive Parentheses parse
while((e.indexOf("(")!=-1) && (e.indexOf(")")!=-1)){
var fail=true;
e=e.replace(/\([\d\:\-±\!\+\/\*\^a-zA-Z\,]*\)/g,function(n){
e=e.replace(/\([^\(\)]*\)/g,function(n){
fail=false;
var h=random_hash();
obj[h]=p(n.substring(1,n.length-1));
Expand Down Expand Up @@ -488,6 +493,7 @@ function p(inp){
}
terms.push(p(be[0]));
terms.push(p(be[1]));

}else if(e.indexOf(":")!=-1){
__debug(!__debug_parser,0) || console.log(spaces.substring(0,level)+"f>: "+e);
terms.type=eqtype.fn;
Expand Down Expand Up @@ -516,11 +522,32 @@ function p(inp){
}else{
var parsednumber=NaN;
if(!isNaN(parsednumber=Number(e))){
terms.type=eqtype.number;
terms.push(parsednumber);
}else if(0){
terms.type=eqtype.constant;
terms.push(e);
return parsednumber;
}else if(!/^hash[a-z\d]{20}hash$/.test(e)){
var match=/^([\d](\.[\d])?)([^\d]+)$/(e);
if(match){
terms.type=eqtype.product;
terms.push(p(match[1]));
terms.push(match[3]);
}else{
var vars=e.split(".");
if(vars.length>1){
terms.type=eqtype.product;
vars.forEach(function(v){
terms.push(p(v));
});
}else{
if(0 && e.length>1 && e[0]=="d"){
terms.type=eqtype.product;
terms.push("d");
terms.push(p(e.substring(1)));
}else{

terms.type=eqtype.variable;
terms.push(e);
}
}
}
}else{
terms.type=eqtype.variable;
terms.push(e);
Expand Down Expand Up @@ -630,9 +657,9 @@ Array.prototype.dot=function(o){
};
Array.prototype.mag=function(){
if(this.type==eqtype.discretevector){
return this.dot(this.conjg()).pow(Num(0.5));
return this.dot(this.conjg()).pow((0.5));
}else{
return this.multiply(this.conjg()).pow(Num(0.5));
return this.multiply(this.conjg()).pow((0.5));
}
};
Array.prototype.conjg=function(){
Expand Down Expand Up @@ -849,17 +876,11 @@ Array.prototype.size=function(){
}
return _size;
};
function Num(x){
return x;
var ar=[x];
ar.type=eqtype.number;
return ar;
}
String.prototype.invert=function(operation){
if(operation==eqtype.sum){
return "-"+this;
}else if(operation==eqtype.sum){
return Num(1).divide(this);
return (1).divide(this);
}else if(operation===undefined){
throw ("Operation not specified");
}
Expand Down Expand Up @@ -1001,6 +1022,11 @@ Number.prototype.factorise=function(){

Array.prototype.factorise=function(){
return this;

//partial fractions (in x)



var right;
if(this.type!=eqtype.sum){
alert("?");
Expand Down Expand Up @@ -1144,12 +1170,13 @@ Array.prototype.inverse=function(){

};
function clean(n){
// de-latexify a string.
for(var i in latexchars){
while(i.length>1 && n.indexOf("\\"+i)!=-1){
n=n.replace("\\"+i,latexchars[i]);
}
}
return n.replace(/\}\{/g,")/(").replace(/\}/g,")").replace(/\{/g,"(").replace(/\\/g,"");;
return n.replace(/\}\{/g,")/(").replace(/\}/g,"))").replace(/\{/g,"((").replace(/\\/g,"");;
}
function p_latex(n){
return p(clean(n));
Expand Down Expand Up @@ -1178,10 +1205,10 @@ function compile(n){
if(eq.length==2){
lhs=p(eq[0]);
var inverselhs=(lhs.dreplace(/y/g,"x")).inverse();
rhs=(inverselhs.dreplace(/x/g,p(eq[1])));
rhs=(inverselhs.dreplace(/x/g,p(eq[1]))).go();
}else{
lhs=p("y"); //This behaviour should be discouraged implicitly.
rhs=p(eq[0]);
rhs=p(eq[0]).go();
}
//compile
var ret={"f":function(){throw("Not a function");}};
Expand Down Expand Up @@ -1217,11 +1244,14 @@ String.prototype.canEval=function(){
if(this[0]=="\"" && this[this.length-1]=="\""){
return true;
}
var isnum=/^[\d\.]+(e[\+\-][\d]+)?$/.test(this.toString());
///var isnum=/^[\d\.]+(e[\+\-][\d]+)?$/.test(this.toString());
var isnum=!isNaN(this.toString());
if(!isnum){
if(!window[this.toString()]){
return false;
}
}else{
console.warn("Number in string: "+this.toString());
}
return true;
};
Expand Down Expand Up @@ -1251,17 +1281,115 @@ String.prototype.simplify=function (){
return this.toString();
};
Number.prototype.simplify=function (){
return this;
};
Number.prototype.go=function(){
return this;
}
String.prototype.go=function(){
return this.toString();
}
String.prototype.has=function(x){
return Number(this.toString()==x);
}
Number.prototype.has=function(x){
return false;
}
Array.prototype.has=function(x){
//has factor. Return +1 if it's there. Return -1 if its in the denomiator. Else return false;

// I suppose we should also:
//return 0 if it is in both.
if(this.type==eqtype.fraction){
var res=0;
if(res=this[0].has(x)){
return res;
}else if(res=this[1].has(x)){
return -res;
}
}else{
var res=0
for(var i=0;i<this.length;i++){
if(res=this[i].has(x)){
return res;
}
}
}
}
Array.prototype.isDifferential=function(){
var self=this.simplify();
if(self.type==eqtype.fraction){
var res;
if( (res = (self[0].has("d") * (self[1].has("dx")))) && !self.search("x")){
return res;
}
if( (res = (self[0].has("dx") * (self[1].has("d")))) && !self.search("x")){
return -res;
}
}
return false;
}
Array.prototype.go=function(){

//performs a mathematical operation, e.g. d/dx (x^2)
var self=this.simplify();
if(self.type==eqtype.product){
var foundit=false;

for(var i=0;i<self.length;i++){
var res;
if(self[i].isDifferential && (res=self[i].isDifferential())){
foundit=res;
self.splice(i,1);
i--;
break;
}
}
if(foundit==1){

return this.simplify().differentiate();
}else if(foundit==-1){
//we have dx/d (f(x)) whatever that means
return undefined;
}

}
if(self.type==eqtype.fraction){
if(self[0].has("d")==1 && self[1].has("dx")==1){
return self.dreplace(/^d$/g,1).dreplace(/^dx$/g,1).simplify().differentiate();
}
}else{
for(var i=0;i<self.length;i++){
if(self[i].go){
self[i]=self[i].go();
}
}
}
return self;
};

Array.prototype.simplify=function (){

if(this.canEval && this.canEval()===true){
return this.eval();
}
if(this.type==eqtype.fn){
this[1]=this[1].simplify();
if(this[0]=="log" && this[1]=="e"){
return 1;
}
return this;
}
if(this.type==eqtype.fraction){
this[0]=this[0].simplify();
this[1]=this[1].simplify();

}
if(this.type==eqtype.power){
this[1]=this[1].simplify();
if(this[1].eval()===1){
return this[0];
}
this[0]=this[0].simplify();
return this;
}
for(var i=0;i<this.length;i++){
while(((typeof e[i]) == "object") && this[i].length==1){
Expand Down Expand Up @@ -1291,6 +1419,32 @@ Array.prototype.simplify=function (){
//Check for singularites
return 0;
}
var newproducts=[];
for(var i=0;i<this.length;i++){
if((typeof this[i]=="object") && this[i].type==eqtype.product){
newproducts.push(this.splice(i,1)[0]);
i--;
}
}
if(newproducts.length){
var self=this;
newproducts.forEach(function(ff){
while(typeof ff=="object" && ff.length==1){
ff=ff[0];
}

ff.forEach(function(gg){
while(typeof gg=="object" && gg.length==1){
ff=ff[0];
}
self.push(gg);
});



});
return self;
}

}else if(this.type==eqtype.sum){
var _prod=0;
Expand Down Expand Up @@ -1347,7 +1501,7 @@ Array.prototype.getString=function(braces,javascript){
}
else if(self.type==eqtype.fn){
if(typeof e !="string" && typeof e!="function"){
throw("function name is not a string!");
throw("function name is not a string: "+e);
return "ERROR";
}
if(functions.indexOf(e)==-1){
Expand Down Expand Up @@ -1397,7 +1551,7 @@ Array.prototype.getString=function(braces,javascript){
};


functions="sin,cos,tan,sec,cot,csc,cosec,log,exp,pow,Gamma,sinc,sqrt,W,fact,bellb,Zeta,u,signum,asin,acos,atan,arcsin,arccos,arctan,tg,ln,abs,floor,round,ceil,atan2,random,min,max,clear,text,shaw,delta".split(",");
functions="sin,cos,tan,sec,cot,csc,cosec,log,exp,pow,Gamma,sinc,sqrt,W,fact,bellb,Zeta,u,signum,asin,acos,atan,arcsin,arccos,arctan,tg,ln,abs,floor,round,ceil,atan2,random,min,max,clear,text,shaw,delta,Γ,ψ".split(",");


var known_derivatives={
Expand All @@ -1411,9 +1565,12 @@ var known_derivatives={
"sqrt":p("(x^(-1/2))*0.5"),
"asin":p("1/sqrt(1-x^2)"),
"acos":p("-1/sqrt(1-x^2)"),
"random":p("(random(x)-0.5)*Infinity")
"fact":p("Γ(x+1)*ψ(x+1)"),
"Gamma":p("Γ(x)*ψ(x)"),
"Γ":p("Γ(x)*ψ(x)")
};

p("(random(x)-0.5)");

if(!this.JSON){this.JSON={}}(function(){function f(n){return n<10?'0'+n:n}if(typeof Date.prototype.toJSON!=='function'){Date.prototype.toJSON=function(key){return isFinite(this.valueOf())?this.getUTCFullYear()+'-'+f(this.getUTCMonth()+1)+'-'+f(this.getUTCDate())+'T'+f(this.getUTCHours())+':'+f(this.getUTCMinutes())+':'+f(this.getUTCSeconds())+'Z':null};String.prototype.toJSON=Number.prototype.toJSON=Boolean.prototype.toJSON=function(key){return this.valueOf()}}var cx=/[\u0000\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g,escapable=/[\\\"\x00-\x1f\x7f-\x9f\u00ad\u0600-\u0604\u070f\u17b4\u17b5\u200c-\u200f\u2028-\u202f\u2060-\u206f\ufeff\ufff0-\uffff]/g,gap,indent,meta={'\b':'\\b','\t':'\\t','\n':'\\n','\f':'\\f','\r':'\\r','"':'\\"','\\':'\\\\'},rep;function quote(string){escapable.lastIndex=0;return escapable.test(string)?'"'+string.replace(escapable,function(a){var c=meta[a];return typeof c==='string'?c:'\\u'+('0000'+a.charCodeAt(0).toString(16)).slice(-4)})+'"':'"'+string+'"'}function str(key,holder){var i,k,v,length,mind=gap,partial,value=holder[key];if(value&&typeof value==='object'&&typeof value.toJSON==='function'){value=value.toJSON(key)}if(typeof rep==='function'){value=rep.call(holder,key,value)}switch(typeof value){case'string':return quote(value);case'number':return isFinite(value)?String(value):'null';case'boolean':case'null':return String(value);case'object':if(!value){return'null'}gap+=indent;partial=[];if(Object.prototype.toString.apply(value)==='[object Array]'){length=value.length;for(i=0;i<length;i+=1){partial[i]=str(i,value)||'null'}v=partial.length===0?'[]':gap?'[\n'+gap+partial.join(',\n'+gap)+'\n'+mind+']':'['+partial.join(',')+']';gap=mind;return v}if(rep&&typeof rep==='object'){length=rep.length;for(i=0;i<length;i+=1){k=rep[i];if(typeof k==='string'){v=str(k,value);if(v){partial.push(quote(k)+(gap?': ':':')+v)}}}}else{for(k in value){if(Object.hasOwnProperty.call(value,k)){v=str(k,value);if(v){partial.push(quote(k)+(gap?': ':':')+v)}}}}v=partial.length===0?'{}':gap?'{\n'+gap+partial.join(',\n'+gap)+'\n'+mind+'}':'{'+partial.join(',')+'}';gap=mind;return v}}if(typeof JSON.stringify!=='function'){JSON.stringify=function(value,dreplacer,space){var i;gap='';indent='';if(typeof space==='number'){for(i=0;i<space;i+=1){indent+=' '}}else if(typeof space==='string'){indent=space}rep=dreplacer;if(dreplacer&&typeof dreplacer!=='function'&&(typeof dreplacer!=='object'||typeof dreplacer.length!=='number')){throw new Error('JSON.stringify');}return str('',{'':value})}}if(typeof JSON.parse!=='function'){JSON.parse=function(text,reviver){var j;function walk(holder,key){var k,v,value=holder[key];if(value&&typeof value==='object'){for(k in value){if(Object.hasOwnProperty.call(value,k)){v=walk(value,k);if(v!==undefined){value[k]=v}else{delete value[k]}}}}return reviver.call(holder,key,value)}text=String(text);cx.lastIndex=0;if(cx.test(text)){text=text.replace(cx,function(a){return'\\u'+('0000'+a.charCodeAt(0).toString(16)).slice(-4)})}if(/^[\],:{}\s]*$/.test(text.replace(/\\(?:["\\\/bfnrt]|u[0-9a-fA-F]{4})/g,'@').replace(/"[^"\\\n\r]*"|true|false|null|-?\d+(?:\.\d*)?(?:[eE][+\-]?\d+)?/g,']').replace(/(?:^|:|,)(?:\s*\[)+/g,''))){j=eval('('+text+')');return typeof reviver==='function'?walk({'':j},''):j}throw new SyntaxError('JSON.parse');}}}());

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