(******************************************************************************
 ** VEC.sml
 ** sml
 **
 ** Franklin Chen and Guy Blelloch 
 ** The VEC signature used as part of the GEOMETRY signature
 ******************************************************************************)

signature VEC =
    sig

        structure Number : NUMBER

	type vec
	type t = vec

        val fromSeq : Number.t Sequence.seq -> t
        val toSeq   : t -> Number.t Sequence.seq
        val == : t * t -> bool
        val != : t * t -> bool

	(* the zero vector *)
	val zero : t

	(* A vector with infinity in each of its dimensions *)
	val infinity : t

	(* add two vectors *)
        val + : t * t -> t

	(* subtract two vectors *)
        val - : t * t -> t

	(* invert a vector *)
        val ~ : t -> t

	(* scale a vector by a number *)
        val scale : t * Number.t -> t

	(* The dot product of two vectors *)
        val dot : t * t -> Number.t

	(* The cross product of dim-1 vectors *)
	val cross : t Sequence.seq -> t

	(* The norm of a vector--i.e. the square root of a vector
	 dotted with itself *)
        val norm : t -> Number.t
       
        val toString : t -> string

    end