import Data.Complex
import Data.List

data Tree a = EmptyTree | Node a (Tree a) (Tree a) deriving (Show)


makePolynominalToTree :: String -> Tree(String)
makePolynominalToTree px =	
	let id = elemIndex '+' px
	    id2 = elemIndex '*' px
	    id3 = elemIndex '^' px 
	in
	case id of	Just a -> Node "plus" (makePolynominalToTree (take a px)) (makePolynominalToTree (drop (a+1) px))
			Nothing -> case id2 of	Just b -> Node "prod" (makePolynominalToTree (take b px)) (makePolynominalToTree (drop (b+1) px))
						Nothing -> case id3 of	Just c -> Node "pow" (makePolynominalToTree (take c px)) (makePolynominalToTree (drop (c+1) px))
									Nothing -> Node px EmptyTree EmptyTree 
			 	
		
makePtreeToFunction :: Tree(String) -> (Complex Float)  -> (Complex Float)
makePtreeToFunction (Node "plus" a b) z = (makePtreeToFunction a z) + (makePtreeToFunction b z)
makePtreeToFunction (Node "prod" a b) z = (makePtreeToFunction a z) * (makePtreeToFunction b z)    
makePtreeToFunction (Node "pow" a b) z = (makePtreeToFunction a z)^(round(magnitude(makePtreeToFunction b z) ))
makePtreeToFunction (Node x EmptyTree EmptyTree ) z  = 	if x == "z" 	then z
									else stringToComplexFloat x

pxtoV :: String -> (Complex Float) -> (Complex Float)
pxtoV s z = makePtreeToFunction (makePolynominalToTree s) z

stringToComplexFloat :: String -> (Complex Float)
stringToComplexFloat s = if ':' `elem` s then read s ::(Complex Float)
					else read (s ++ ":+ 0.0") ::(Complex Float)