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Source code for Vitaliy's Math Javascript Library - UPDATE:

<html>
<head>
	<title>Vitaliy's Math Javascript Library Demo</title>

<script language="JavaScript">
<!--
/************************************************************************************/
/* math.js - the library of mathematical functions that are not part of Math object.*/
/* AUTHOR: Vitaliy Rabotnik WWW: http://chat.carleton.ca/~vrabotni/JavaScript/Math/ */
/* PLEASE KEEP THE REFERRENCE TO MY WEB SITE, SO THAT PEOPLE COULD GET UPTODATE     */   
/* VERSION                                                                          */
/* VERSION: 1                                               DATE: 01/03/2000        */
/************************************************************************************/

/****************************************************************************/
/* DESCRIPTION: Returns a string representing expansion of (x + y)^n.       */
/* PARAMETERS: n - a positive integer;                                      */
/* format(optional) - the output format either text ("txt") or html ("html")*/
/* default is "html" format                                                 */
/****************************************************************************/
function binomial(n, format)
{
  var out = "";
  var temp;
  var pow1, pow2;
  
  if(format == "txt")
  {
    pow1 = "^";
	pow2 ="";
  }
  
  else
  {
    pow1 = "<sup>";
	pow2 = "</sup>";	  
  }
  
  if(!isInteger(n) || n < 0) 
  {
   // alert("Error \"binomial\": " + n + " is not valid number.");
    return;
  }
  
  for(var i = 0; i <= n; i++)
  {
    temp = choose(n,i);

if(temp > 1)
	 out += temp;
	
	if(i > 1)
	  out += "x" + pow1 + i + pow2;

if(i == 1)
	  out += "x";
	  
	if(n - i > 1)
	 out += "y" + pow1 + (n - i) + pow2;
	 
	if(n - i == 1)
	 out += "y";
	 
	if(i < n)
	 out += " + ";    
  }
  return out;
}

/*******************************************************************************************/
/* DESCRIPTION: Returns the result of  "n choose r"; Returns null if "n" and r are invalid.*/
/* PARAMETERS: n and r - are positive integers, where r is less or equal to n.             */
/*******************************************************************************************/
function choose(n,r)
{
  if(!isInteger(n) || !isInteger(r))
  {
   // alert("Error \"choose\": " + n + " or " + r + " are not valid number.");
    return;
  }
  
  if(r > n)
  {
    // alert("Error \"choose\": " + r + " must be less or equal to " + n + ".");
	 return;
  }
  
  return factorial(n)/(factorial(n - r) * factorial(r));
}

/************************************************************************************/
/* DESCRIPTION: Returns the factorial of namber "n"; Returns null if "n" is invalid.*/
/* PARAMETERS: n - a positive integer                                               */
/************************************************************************************/
function factorial(n)
{
  if(n < 0 || !isInteger(n)) 
  {
   // alert("Error \"factorial\": " + n + " is not valid number.");
    return;
  }
  if(n == 0) return 1;
  if(n == 1) return n;
  return (n * factorial(n - 1));
}

/*******************************************************************************/
/* DESCRIPTION: Returns n th fibonacci number; Returns null if "n" is invalid. */
/* PARAMETERS: n - a positive integer greater than zero                        */
/*******************************************************************************/
function fibonacci(n)
{
  if(n < 1 || !isInteger(n)) 
  {
   // alert("Error \"fibonacci\": " + n + " is not valid number.");
    return;
  }

if(n == 1 || n == 2)  
    return 1;

return fibonacci(n - 1) + fibonacci(n - 2);	
}

/********************************************************************/
/* DESCRIPTION: Returns wheather the number "n" is an even number.  */
/* PARAMETERS: n - an integer or a string representing integer.     */
/********************************************************************/
function isEven(n)
{
  if(!isInteger(n))  
  {
  // alert("Error \"roundOff\": " + n + " or " + r + " is not valid number.");
    return;
  }
  
  return(n%2 == 0);
}

/*************************************************************/
/* DESCRIPTION: Returns wheather the number "n" is a float.  */
/* PARAMETERS: n - a float or a string representing float.   */
/*************************************************************/
/*
function isFloat(n)
{
  return (parseFloat("" + n) === n);
}  
*/

/******************************************************************/
/* DESCRIPTION: Returns wheather the number "n" is an integer.    */
/* PARAMETERS: n - an integer or a string representing integer.   */
/******************************************************************/
function isInteger(n)
{
   if(isNaN(n))
     return false;
	 
   return(parseInt("" + n) == n);
}

/******************************************************************/
/* DESCRIPTION: Returns wheather the number "n" is a prime number.*/
/* PARAMETERS: n - a positive integer greater than zero.          */
/******************************************************************/
function isPrime(n)
{
  if(!isInteger(n) || n < 1) 
  {
   // alert("Error \"isPrime\": " + n + " is not valid number.");
    return;
  }
    
  for(var i = 2; i < n - 1; i++) 
  {
    if(n % i == 0)
	  return false;
  }
  return true;
}

/********************************************************************/
/* DESCRIPTION: Returns wheather the number "n" is an odd number.   */
/* PARAMETERS: n - an integer or a string representing integer.     */
/********************************************************************/
function isOdd(n)
{
  if(!isInteger(n))  
  {
  // alert("Error \"roundOff\": " + n + " or " + r + " is not valid number.");
    return;
  }

return(!isEven(n));
}

/********************************************************************/
/* DESCRIPTION: Logarithm of number "n" to the base a.              */
/* PARAMETERS: n - a number; a - base.                              */
/********************************************************************/
function log(n,a)
{
  if(isNaN(a) || isNaN(n))
    return;

return(Math.log(n)/Math.log(a));
}

/*********************************************************************/
/* DESCRIPTION: Rounds off the number "n" to "digits" decimal places.*/
/* PARAMETERS: n - a number; digits - number of decimal places.      */
/*********************************************************************/
function roundOff(n,digits)
{
  var temp;

if(isNaN(n) || !isInteger(digits))  
  {
  // alert("Error \"roundOff\": " + n + " or " + r + " is not valid number.");
    return;
  }
  
  if(digits < 0)
  {
    // alert("Error \"roundOff\": " + digits + " must be greater or equal to zero.");
    return null;
  }

if(digits == 0)
    return Math.round(n);
  
  temp =  Math.pow(10,digits)
 
  return(Math.round(n * temp)/temp);
}

/********************************************************************************/
/* DESCRIPTION: Returns a string representation of the binary convertion of "n".*/
/* PARAMETERS: n - a positive integer.                                          */
/********************************************************************************/
function toBinary(n)
{
  var out = "";
  var temp;
    
  if(!isInteger(n) || n < 0) 
  {
   // alert("Error \"toBinary\": " + n + " is not valid number.");
    return;
  }
  if(n == 0)
   return 0;
  
  temp = n;
  while(temp > 0)
  {
    out =  (temp % 2) + out; 
    temp = parseInt(temp / 2);
  } 
  return out;
}

/********************************************************************************/
/* DESCRIPTION: Returns an integer.                                             */
/* PARAMETERS: n - a string representation of the binary number.                */
/********************************************************************************/
function toDecimal(n)
{
  var out = 0;
  var temp = "";
  var startFound = false;
      
  temp += n;
  
  if(!validBinaryNumber(temp))
    return;
	
  for(var i = 0; i < temp.length; i++) 
  {
    if(temp.charAt(i) == '1')
	  startFound = true;
	  
    if(startFound)
      out += parseInt(temp.charAt(i)) * Math.pow(2, temp.length - (i + 1));
  }	
  return out;
}

function validBinaryNumber(n)
{
  for(var i = 0; i< n.length; i++)
  {
    if(n.charAt(i) != '0' && n.charAt(i) != '1')
	  return false;
  }
  return true;	  
}

//-->
</script>
<script language="JavaScript">

var functionNames;
var rules;
var farguments;
var n, r;

var IE = document.all;
var NS = document.layers;

function setText(what,str)
{
  if(IE)
    what.innerHTML = str;

else if(NS)	
  {
    what.document.open();
    what.document.write(str);
	what.document.close();
  }	
}

function getInput()
{
  var f = document.forms[0];
  var list = f.functions;
  var args = farguments[list.selectedIndex];
  var func = functionNames[list.selectedIndex];
  var type = inputTypes[list.selectedIndex];
  
   n = prompt("Please enter the value for n: ", "");
	
   if(n == null)
   {
	  alert("The action was aborted by user!")
	  return;
	}

if(type[0] == "int")   
      n = parseInt(n);
	  
	else if (type[0] == "float")
	  n = parseFloat(n);  
 
   if(args == 2)
   {
      r = prompt("Please enter the value for r: ", "");
	
     if(r == null)
     {
	  alert("The action was aborted by user!")
	  return;
     }

if(type[1] == "int")   
       r = parseInt(r);
	  
	else if (type[1] == "float")
	  r = parseFloat(r);  
   }

solve(func,args);   
}

function solve(func, args)
{
 var field = getField("answ");
 var msg = "<b>Answer is:</b> ";
 
 if(args == 1)
 {
   if(isNaN(n))
     msg += eval(func + "(\"" + n + "\")");
   else 	 
     msg += eval(func + "(" + n + ")");
  }
  else if(args == 2)
    msg +=  eval(func + "(" + n + "," + r + ")");
  setText(field, msg);
}

function update(ptr)
{
   var index = ptr.selectedIndex;
   setText(getField("description"), rules[index]);
   setText(getField("answ"), "");
}

function getField(name)
{
   if(IE)
    return document.all[name];

else if(NS)	
   {
    return document.layers[name];
   }	
}

// add an Option object into a combo box at index
function addOption(list, index, opt)
{
   list.options[index] = opt;
}

// fill up a combobox with Option objects
function fillUpList(list, options, values)
{
   for(var i = 0; i < options.length; i++)
      addOption(list, i, new Option(options[i]),values[i]);
   list.selectedIndex =  0; 
}

function fixStupidNetscapeBug()
{
    var pointer = document["ptr"];
	var troubleLayer = document.layers["answ"];
	
	troubleLayer.top = pointer.pageY;
	troubleLayer.left = pointer.pageX;
}
</script>
</head>
<body onload="init();">
<center><h2>Vitaliy's Math Javascript Library Demo</h2></center>
<P>
<b>Vitaliy's Math Javascript Library</b> - is the collection of mathematical 
routines not included in JavaScript built-in objects (Math, Number).
The tool on this page is used to demonstrate how these functions work.
This is still a beta version of the library, since testing is not complete yet.
<P>
<form>
<table cellspacing="7" cellpadding="7">
<tr>
<td><select name="functions" onChange="update(this);">
<option value>[empty1]</option>
<option value>[empty2]</option>
<option value>[empty3]</option>
</select>
<input type="button" value="Calculate" onClick="getInput();"></td>
<td><span id="answ"><ilayer name="ptr"></ilayer><layer name="answ"></layer></span></td>
</tr></table><P>
<span id="description"><layer name="description"></layer></span>
</form>

<script language="JavaScript">
function init()
{
   var f = document.forms[0];
   
   functionNames = new Array("binomial", "choose", "factorial", "fibonacci", "isEven", "isInteger", "isPrime", "isOdd", "log", "roundOff", "toBinary", "toDecimal");
   rules = new Array();
   
   rules[0] = "<b>binomial(n)</b> - returns binomial expansion of equation (x + y)<sup>n</sup>.<br><i>n</i> must be a positive integer.";
   rules[1] = "<b>choose(n,r)</b> - returns number of different groups of size <i>r</i> selected from a set of <i>n</i> objects, where <i>r <= n</i>.";
   rules[2] = "<b>factorial(n)</b> - returns a factorial of the number <i>n</i>. <br><i>n</i> must be a positive integer.";
   rules[3] = "<b>fibonacci(n)</b> - returns <i>n<sup>th</sup></i> fibonacci number. <br><i>n</i> must be a positive integer.";
   rules[4] = "<b>isEven(n)</b> - whether <i>n</i> is an even number.<br><i>n</i> must be an integer.";
   rules[5] = "<b>isInteger(n)</b> - whether <i>n</i> is an integer.";
   rules[6] = "<b>isPrime(n)</b> - whether <i>n</i> is a prime number.<br><i>n</i> must be an integer greater than zero.";
   rules[7] = "<b>isOdd(n)</b> - whether <i>n</i> is an odd number.<br><i>n</i> must be an integer.";
   rules[8] = "<b>log(n,r)</b> - returns logarithm of <i>n</i> to the base <i>r</i>.";
   rules[9] = "<b>roundOff(n,r)</b> - rounds off <i>n</i> to specified (<i>r</i>) number of digits.";
   rules[10] = "<b>toBinary(n)</b> - returns a string representing binary number conversion of <i>n</i>.<br><i>n</i> must be a positive integer.";
   rules[11] = "<b>toDecimal(n)</b> - returns a decimal integer representation of binary string <i>n</i>.<br><i>n</i> must be a valid binary string.";
   
   farguments = new Array(1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1);   
    
   inputTypes = new Array();
   inputTypes[0] = new Array("int");
   inputTypes[1] = new Array("int","int");
   inputTypes[2] = new Array("int");
   inputTypes[3] = new Array("int");
   inputTypes[4] = new Array("int");
   inputTypes[5] = new Array("any");
   inputTypes[6] = new Array("int");
   inputTypes[7] = new Array("int");
   inputTypes[8] = new Array("float", "float");
   inputTypes[9] = new Array("float","int");
   inputTypes[10] = new Array("int");   
   inputTypes[11] = new Array("str");  
   
   fillUpList(f.functions, functionNames, functionNames);
   setText(getField("description"), rules[0]);
   
   if(NS)
    fixStupidNetscapeBug();
}
</script>
</body>
</html>

*JavaScript is a registered trademark of Sun Microsystems, Inc.

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