module Exercise_6 where

import Data.Ratio

{-WETT-}
                
traceFractran :: [Rational] -> Integer -> [Integer]
traceFractran xs n = let pass = [numerator x * n `div` denominator x|x<-xs, n`mod`denominator x == 0] in [n] ++ if pass /= [] then traceFractran xs (head pass) else []

{-TTEW-}

--isPowerOfTwo :: Integer -> Bool
--isPowerOfTwo x
--    | x == 2 = True
--    | x `mod` 2 == 0 = True && isPowerOfTwo (x `div` 2)
--    | otherwise = False
--
--traceFractran2 :: [Rational] -> Integer -> [Integer]
--traceFractran2 xs n = aux xs xs n
--        where 
--            aux [] ys n = [n]
--            aux (x:xs) ys n 
--                | n `mod` (denominator x) == 0 && n > 0 = [n] ++ traceFractran2 ys ((numerator x * n)`div`(denominator x))
--                | otherwise = aux xs ys n
                
-- [numerator x * n `div` denominator x|x<-xs, n`mod`denominator x == 0]]
--traceFractran xs n = let pass = [numerator $ x*fromInteger n|x<-xs, denominator (x*fromInteger n) == 1] in if pass /= [] then [n] ++ traceFractran xs (head pass) else [n]
--traceFractran xs n = let pass = [numerator x*n|x<-xs, denominator (x*n) == 1] in if pass /= [] then [n] ++ traceFractran xs (head pass) else [n]