qnikst

gauss  :: [[Double]] -> [Double]
gauss  m = let (m',is) = gauss0 m
           in order is $ gauss2 $ gauss1 m

gauss0 :: [[Double]] -> ([[Double]],[Int])
gauss0 m = let (     mt,is) = foldr choose (trns m,straight) straight
           in  (trns mt,is)
    where choose k  (mt,is) = let row = m !! (k-1)
                                  q   = (+) 1 $ fromJust $ elemIndex (maximum $ init $ drop (k-1) row) row
                              in (swap' k q mt, swap' k q is)