functor VECTOR( structure Complex : ComplexSig) : VectorSig  =
struct
open Complex;

type scalar = complex
type vector = complex * complex
type matrix = vector * vector

fun  vector (x,y) = (x,y)
fun  matrix (a,b) = (a,b)

fun scale (s,(a,b))   = vector (s ** a, s ** b)
fun (a,b) dot (a',b') = a ** a' ++ b ** b'
fun apply ((a,b),v)   = vector (a dot v, b dot v)
end;