module MyDet where

type Matrix = [[Rational]]

first :: [[a]] -> [a]
first [] = []
first (xs:_) = xs

pad a = [x ++ x | x <- a]

sig n = case odd n of
           True -> -1
	   False -> 1

ind :: Int -> Int -> Matrix -> Rational
ind i k mat = (mat !! (i-1)) !! (k-1)

slice :: (Int,Int) -> (Int,Int) -> Matrix -> Matrix
slice (i,j) (k,l) mat
    = let rowSliceFront = drop (i-1) mat
          rowSlice      = take (k-i+1) rowSliceFront
	  columnSliceFront = map (drop (j-1)) rowSlice
      in map (take (l-j+1)) columnSliceFront

determinant :: Matrix -> Rational
determinant mat = det (pad mat) (length mat)

det :: Matrix -> Int -> Rational
det mat 1 = ind 1 1 mat
det mat size
    = let coeffs = zipWith (*) (cycle [1,sig newsize]) $ first mat
          newsize = size - 1
	  leastToMax = newsize - 1
	  slices = [slice (2,i) (size,i+leastToMax) mat | i <- [2 .. (size+1)]]
      in sum (zipWith (*) coeffs (map (\l -> det l newsize) (map pad slices)))