<?php
//!--------------------------------------------------------
// @class		bNewton
// @desc		Solve the Newton's binomial.
//				Use the binomial theorem to solve and
//				to display the equation.
//				Solving the binomial coefficients it show 
//				the equivalent equation.
// @author		Israel de Souza Rocha
//!--------------------------------------------------------

class bNewton {

	//!--------------------------------------------------
	// @function	bNewton::calculate
	// @desc		Main class method. Calculate and dislplay 
	//				the result.
	// @param		a string	first binomial's element
	// @param		b string	second binonial's element
	// @param		grade int	binomial's grade
	// @access		public
	// @return		void
	//!--------------------------------------------------
	function calculate($a, $b, $grade) {
		$res = $a . '<sup>' . $grade . '</sup>';
		$negative = (trim($b[0])=='-');
		if ($negative) {
			$b = substr($b, 1, strlen($b));
		}
		$signal = '+';
		for ($i = 1; $i < $grade; $i++) {
			$signal = (($negative) ? $this->signal(&$negative) : $signal);
			$res .= $signal . ' ' . $this->binomialNumber($grade, $i) . ' . ' . $a . '<sup>' . (($grade - $i == 1) ? '' :$grade - $i) . '</sup> . ' . $b . '<sup>' . (($i==1) ?'':$i)  . '</sup> ';
		}
		$signal = (($negative) ? $this->signal(&$negative) : $signal);
		$res .= $signal . ' ' . $b . '<sup>' . $grade . '</sup>';
		echo $res;
	}

	//!--------------------------------------------------
	// @function	bNewton::binomialNumber
	// @desc		Used to calculate the binomial coefficient.
	// @param		n int			
	// @param		p int
	// @access		public
	// @return		int
	//!--------------------------------------------------	
	function binomialNumber($n, $p) {
		return $this->fat($n) / ( $this->fat($p) * $this->fat($n - $p) );
	}
	
	//!--------------------------------------------------
	// @function	bNewton::fat
	// @desc		Simple factorial.
	// @param		val int		Number to factorate
	// @param		pos string	Position to calculate the next value
	// @access		public
	// @return		int
	//!--------------------------------------------------	
	function fat( $val, $pos = null ) {
		$pos = ($pos == null) ? $val : $pos;
		if ($pos != 1) {
			return $this->fat($val * ($pos - 1), $pos -1);
		}
		return $val;
	}

	//!--------------------------------------------------
	// @function	bNewton::signal
	// @desc		Alternate the binomial's terms signal.
	// @param		sig string	The signal
	// @access		public
	// @return		string
	//!--------------------------------------------------	
	function signal($sig) {
		if ($sig=='-') {
			$sig = '+';	
		} else {
			$sig = '-';	
		}
		return $sig;
	}
}
?>