caret (^) to pow() function

[djh101]

Having to work with derivatives a lot, I made this nice, simple function for converting a^b form exponents in strings to eval'able pow(a,b) form. Enjoy.

PHP Code:

function carToPow($expression){
    //array of positions: start of base, position of ^, end of power
    $pos = array(null,null,null);
    //array of parts: base and power
    $parts = array();
    
    for($i=0; $i<strlen($expression); $i++){
        
        if($expression[$i] === '^'){
            $pos[1] = $i;
            
            //scan for base
            if($expression[$i-1] === ')'){ //base is a function
                $depth = 0;
                for($j=$i-1; $j >= 0; $j--){
                    if($expression[$j] === ')') $depth++;
                    if($expression[$j] === '(') $depth--;
                    if($depth == 0){
                        $pos[0] = $j;
                        $parts[0] = substr($expression, $j, $i-$j);
                        break;
                    }
                }
            } else if($expression[$i-1] === 'x'){ //base is a variable
                $pos[0] = $i-1;
                $parts[0] = "x";
            } else { //base is a number
                if(preg_match("/\\d*\\.{0,1}\\d+\\^/",$expression,$foo)){
                    $pos[0] = $i - strlen($foo[0]) + 1;
                    $parts[0] = substr($foo[0],0,strlen($foo[0])-1);
                } else return false;
            }
            
            //scan for power
            if($expression[$i+1] === '('){ //power is a function
                $depth = 0;
                for($j=$i+1; $j < strlen($expression); $j++){
                    if($expression[$j] === '(') $depth++;
                    if($expression[$j] === ')') $depth--;
                    if($depth == 0){
                        $pos[2] = $j;
                        $parts[1] = substr($expression, $i+1, $j-$i);
                        break;
                    }
                }
            } else if($expression[$i+1] === 'x'){ //base is a variable
                $pos[2] = $i+1;
                $parts[1] = "x";
            } else { //power is a number
                if(preg_match("/\\^\\d*\\.{0,1}\\d+/",$expression,$foo)){
                    $pos[2] = $i + strlen($foo[0]) - 1;
                    $parts[1] = substr($foo[0],1,strlen($foo[0])-1);
                } else return false;
            }
            
            if($parts[0] == null || $parts[1] == null) return false;
            $expression = substr($expression,0,$pos[0]).'pow('.$parts[0].','.$parts[1].')'.substr($expression,$pos[2]+1,strlen($expression)-$pos[2]);
            return ($expression = carToPow($expression)) ? $expression : false;
            
        }
        
    }
    return $expression;
    
} 


[Fou-Lu]

I don't know if I'd recommend that the caret be replaced since you'll lose the concept of the xor, but why not just use a regex to match it completely?

PHP Code:

$sEquation = '452.2 ^ x + 14 - y';

$sPattern = '/([a-z]|\d+(?:\.\d+)?)*\s*\^\s*([a-z]|\d+(?:\.\d+)?)/i';
$sReplace = 'pow($1, $2)';

$sResult = preg_replace($sPattern, $sReplace, $sEquation);

print $sResult; 


That will give you the same result. Granted without using a stack for this, the behaviour becomes slightly unusual if you provide an unmarked multiplication.

[djh101]

This is intended for strings of standard math functions, where ^ is used for exponential expressions (and xor is not used at all). Your code works fine for standard a^b expressions, but the stack is needed for converting functions where the base or exponent is a parenthetical expression.

[Fou-Lu]

Ooh yeah I do see what you mean, never thought about parenthetical expressions for the exponent, and its a mess if you have pow of pow (...of pow...*).
I know this can be done in regex as well, but I'm afraid that's beyond my skills as a matcher for sure. Stack handling even iterating is probably faster than the pattern would be anyway.