```
(* Calcul matriciel

Variante du programme 83 page 333, paramétré par le type des éléments *)

module Matrix
(X : sig
type t
val zero : t
val one : t
val add : t -> t -> t
val sub : t -> t -> t
val mul : t -> t -> t
end) =
struct

type t = X.t array array

let init_matrix n m f =
Array.init n (fun i -> Array.init m (fun j -> f i j))

let id n =
init_matrix n n (fun i j -> if i = j then X.one else X.zero)

let size a =
(Array.length a, Array.length a.(0))

let (n, m) as s = size a in
if size b <> s then invalid_arg "add";
init_matrix n m (fun i j -> X.add a.(i).(j) b.(i).(j))

let sub a b =
let (n, m) as s = size a in
if size b <> s then invalid_arg "sub";
init_matrix n m (fun i j -> X.sub a.(i).(j) b.(i).(j))

let mul a b =
let n, p = size a in
let q, m = size b in
if q <> p then invalid_arg "mul";
let product i j =
let s = ref X.zero in
for k = 0 to p - 1 do s := X.add !s (X.mul a.(i).(k) b.(k).(j)) done;
!s
in
init_matrix n m product

end
```

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