module SetRing (F : FiniteRing) : Ring with type t = F.t list = struct
  type t = F.t list
  let zero = []
  let one = F.elems
  let compare a b = let rec innercomp a b = match (a,b) with
   | (x1::xs1, x2::xs2) -> if ((F.compare x1 x2) == 0) then (innercomp xs1 xs2) else F.compare x1 x2
   | (x1::xs1, []) -> 1
   | ([], x2::xs2) -> -1
   | ([], []) -> 0
    in
    innercomp (List.sort F.compare a) (List.sort F.compare b)

  let to_string a = let rec inner a = match a with
    | [] -> ""
    | [x] -> F.to_string x
    | x::xs -> F.to_string x ^ "," ^ (inner xs)
    in
    "{" ^ (inner a) ^ "}"
  let rec add a b = let rec inner a = match a with
    | [] -> []
    | x::xs -> if (List.mem x xs) then inner xs else x::(inner xs)
    in
    inner (a @ b)
  let rec mul a b = match a with
    | [] -> []
    | x::xs -> if (List.mem x b) then x::(mul xs b) else mul xs b
end