Modular Arithmetic

let (%) (a,b) c = (a*b) mod c ;;

let print_list l = print_string "["; List.iteri (fun i x -> if i+1=List.length l then print_int x else
    (print_int x; print_string "; ")) l; print_string "]";;
let print_list_of_lists l = List.iter (fun lt -> print_list lt; print_string ";   \n") l ;;

let rec repeat n(*раз*) x = if n<=0 then [] else x :: (repeat (n-1) x) ;;

let classes n = List.mapi (fun i z1 -> (i,List.mapi (fun j z2 -> (i*j) mod (n)) (repeat n 0))) (repeat n 0) ;;

let rec find_i (i,l) = match l with
    | [] -> []
    | (a,lst) :: t -> if a=i then lst else find_i (i,t) ;;

let rec find x l = match l with
    | [] -> false
    | a :: b -> if a=x then true else find x b ;;

let rec liberty l = match l with
    | [] -> []
    | -1 :: t -> liberty t
    | a :: b -> if find a b = true then liberty b else a :: (liberty b) ;;

let generator l = let help () = List.map (fun (i,x) -> List.map (fun y ->
        if find i (find_i (y,l))=true then y else -1) x) l in (List.map (fun l -> liberty l) (help ())) ;;

let rec nlib lst =
    match lst with
    | [] -> []
    | a :: b -> a@(nlib b) ;;

print_string "Введите n : " ;;
let n = read_int () ;;
let all_classes_by_n = (generator (classes n));;

let associativity l = List.for_all (fun (x,y,z) -> if (x,(y,z)%n)%n=((x,y)%n,z)%n then true else false)
    (nlib (List.map (fun a -> nlib (List.map (fun b -> List.map (fun c -> (a,b,c)) l) l)) l)) ;;

let identity_element l = if (List.map (fun x -> if (List.exists (fun y -> if (x,y)%n=y then true else false) l) = true
    then x else -1) l) <> [] then true else false ;;

let id_element l = let lst=liberty (List.map (fun x -> if (List.exists (fun y -> if (x,y)%n=y then true else false) l) = true
    then x else -1) l) in if lst=[] then -1 else List.nth lst 0 ;;

let closure l = List.for_all (fun (x,y) -> find ((x,y)%n) l) (nlib (List.map (fun i -> List.map (fun j -> (i,j)) l) l)) ;;

let inverse_element l = if identity_element l then List.for_all (fun a -> List.exists
    (fun b -> if (a,b)%n=(id_element l) then true else false) l) l
    else false ;;

List.iter (fun classes_by_n -> print_list classes_by_n;
let p1 = associativity classes_by_n in ( let p2 = identity_element classes_by_n in ( let p3 = closure classes_by_n in (
    let p4 = inverse_element classes_by_n in (
    if p1 then print_string "\t - Есть ассоциативность;  " else print_string "\t - Ассоциативности нет; ";
    if p2 then print_string "\tЕсть нейтральный; " else print_string "\tНет нейтрального; ";
    if p3 then print_string "\tЕсть замкнутось; " else print_string "\tНет замкнутости; ";
    if p4 then print_string "\tЕсть обратимость; " else print_string "\tНет обратимости; ";
    if p1 && p2 && p3 && p4 then print_string "\tЭто группа\n" else print_string "\tЭто не группа\n"
    ) )))) all_classes_by_n ;;