(** Encodes the powers of x, y, z in a compact form, suitable for being
  used in a hash table.
  *)

type t 

val to_string : t -> string
(** Pretty printing *)

val of_powers_three  : Powers.t -> t
(** Create from a {!Powers.t}. *)

val of_powers_six    : Powers.t -> Powers.t -> t
(** Create from two {!Powers.t}. *)

val of_powers_nine   : Powers.t -> Powers.t -> Powers.t -> t
(** Create from three {!Powers.t}. *)

val of_powers_twelve : Powers.t -> Powers.t -> Powers.t -> Powers.t -> t
(** Create from four {!Powers.t}. *)

type kind =
  | Three  of  Powers.t
  | Six    of (Powers.t * Powers.t)
  | Nine   of (Powers.t * Powers.t * Powers.t)
  | Twelve of (Powers.t * Powers.t * Powers.t * Powers.t)

val of_powers : kind -> t
(** Create using the [kind] type *)

val to_int_array : t -> int array
(** Convert to an int array. *)

val to_powers : t -> kind

(** {1 Functions for hash tables} *)

val hash : t -> int
(** Associates a nonnegative integer to any Zkey. *)

val equal : t -> t -> bool
(** The equal function. True if two Zkeys are equal. *)

val compare : t -> t -> int
(** Comparison function, used for sorting. *)