(** Azimuthal quantum number, represented as s,p,d,... *)

type t = S | P | D | F | G | H | I | J | K | L | M | N | O

exception AngularMomentumError of string
(** Raised when the {!AngularMomentum.t} element can't be created.
  *)

val of_char : char -> t
(** Returns an {!AngularMomentum.t} when a shell is given as a character (case
  insensitive).

  Example:

  [AngularMomentum.of_char 'p' -> AngularMomentum.P]
 *)

val to_string : t -> string
(** 
  [AngularMomentum.(to_string D) -> "D"]
 *)


val to_char : t -> char
(** 
  [AngularMomentum.(to_char D) -> 'D']
 *)


val to_int : t -> int
(** 
  Returns the l{_max} value of the shell.

  Example:

  [AngularMomentum.of_int 3 -> AngularMomentum.F]
 *)

val of_int : int -> t
(** 
  Opposite of {!of_int}.

  Example:

  [AngularMomentum.of_int 3 -> AngularMomentum.F]
 *)

type kind =
    Singlet of t
  | Doublet of (t * t)
  | Triplet of (t * t * t)
  | Quartet of (t * t * t * t)


val n_functions : t -> int
(** Number of cartesian functions in shell.

  Example:

  [AngularMomentum.n_functions D -> 6]
  *)


val zkey_array : kind -> Zkey.t array
(** Array of {!Zkey.t}, where each element is a a key associated with the
  the powers of x,y,z.

  Example:

  {[
  AngularMomentum.( zkey_array Doublet (P,S) ) ->
    [| {Zkey.left = 0; right = 1125899906842624} ;
       {Zkey.left = 0; right = 1099511627776}    ;
       {Zkey.left = 0; right = 1073741824}       |] 
  =
 
  let s,x,y,z =
      Powers.( of_int_tuple (0,0,0),
               of_int_tuple (1,0,0),
               of_int_tuple (0,1,0), 
               of_int_tuple (0,0,1) ) 
  in
  Array.map (fun (a,b) -> {!Zkey.of_powers_six} a b)
      [| (x,s) ; (y,s) ; (z,s) |]
  ]}

  *)