main :: [sys_message]
main = [Stdout (lay (map lincomb tests))]
       where tests = [[1,2,3], [0,1,2,3], [1,0,3,4], [1,2,0], [0,0,0],
                      [0], [1,1,1], [-1,-1,-1], [-1,-2,0,-3], [-1]]

lincomb :: [num]->[char]
lincomb xs = "0", if result = ""
           = result, otherwise
             where result = foldl term "" (zip2 [1..] xs)
                   term r  (i,0)  = r
                   term "" (i,-1) = "-" ++ te i
                   term "" (i,1)  = te i
                   term "" (i,n)  = "-" ++ show (abs n) ++ "*" ++ te i, if n<0
                                  = show n ++ "*" ++ te i, otherwise
                   term r  (i,-1) = r ++ " - " ++ te i
                   term r  (i,1)  = r ++ " + " ++ te i
                   term r  (i,n)  = r ++ sgn ++ show (abs n) ++ "*" ++ te i
                                    where sgn = " - ", if n<0
                                              = " + ", otherwise
                   te n = "e(" ++ shownum n ++ ")"