<?php
class Monomial {
	var $numeric_factor = 1;
	var $vars = array();
	// 5a^2, n_f = 5, vars = array('a' => 2);
	function mul(Monomial $b, $is_div = false) {
		$nf = $this->numeric_factor * $b->numeric_factor;
		$nv = array();
		foreach($this->vars as $var => $exp) {
			if(isset($b->vars[$var])) {
				if($is_div) {
					$nv[$var] = $exp - $b->vars[$var];
				} else {
					$nv[$var] = $exp + $b->vars[$var];
				}
			}	else {
				$nv[$var] = $exp;
			}
		}
		foreach($b->vars as $var => $exp) {
			if(!isset($nv[$var])) {
				if($is_div) {
					throw new Exception('Illegal monomial division');
				} else {
					$nv[$var] = $exp;
				}
			}
		}
		$this->numeric_factor = $nf;
		$this->vars = $nv;
	}
	function mulf(Monomial $b, $is_div = false) {
		$m = clone $this;
		$m->mul($b, $is_div);
		return $m;
	}
	function div(Monomial $b) {
		$this->mul($b, true);
	}
	function divf(Monomial $b) {
		return mulf($b, true);
	}
	function remove_var_1($res) {
		$v = $res[1];
		$n = $res[2];
		if(!isset($this->vars[$v])) $this->vars[$v] = 0;
		$this->vars[$v] += $n;
	}
	function remove_var_2($res) {
		$this->remove_var_1(array(0, $res[0], 1));
	}
	function Monomial($str='') {
		$str = preg_replace_callback('/([a-z])\^([0-9]+)/i', array($this, 'remove_var_1'), $str);
		$str = preg_replace_callback('/[a-z]/i', array($this, 'remove_var_2'), $str);
		$str = trim($str);
		if(is_numeric($str)) {
			$this->numeric_factor = (real) $str;
		} else if($str == '') {
			$this->numeric_factor = 1;
		} else {
			throw new Exception('Nonnumeric final string ' . $str);
		}
	}
	function to_str() {
		$str = (string) $this->numeric_factor;
		foreach($this->vars as $v => $e) {
			if($e == 1) {
				$str .= $v;
			} else {
				$str .= "$v^$e";
			}
		}
		return $str;
	}
}
$x = new Monomial('7a^2b^3cd^4');
echo "Original is:\n";
echo $x->to_str() . "\n";
$mul = new Monomial('14bc^2');
echo "Multiply by:\n";
echo $mul->to_str() . "\n";
$x->mul($mul);
echo "Final is:\n";
echo $x->to_str() . "\n";
?>