signature vecfun=
sig
 type vectfun
val makevfun :(real->real->real ->real)*(real->real->real 
->real)*(real->real->real ->real) ->vectfun
val add :vectfun*vectfun ->vectfun
val diff :vectfun*vectfun ->vectfun
val dot :vectfun*vectfun ->(real->real->real ->real)
val cross :vectfun*vectfun ->vectfun
val curl :vectfun ->vectfun
val dvg :vectfun ->real->real->real -> real
end

structure Vfun :vecfun=
struct
 datatype vectfun= VEC of (real->real->real ->real)*(real->real->real 
->real)*(real->real->real ->real)
 fun makevfun(a,b,c)=VEC(a,b,c)
 fun fsum a b (x:real)  (y:real) (z:real) =((a x y z ) +(b x y z)) :real 
 fun fdiff a b (x:real)  (y:real) (z:real)=((a x y z ) -(b x y z)) :real
 fun fmult a b (x:real)  (y:real) (z:real) =((a x y z )*(b x y z)) :real 
 fun 
add(VEC(ax,ay,az),VEC(bx,by,bz))=VEC((fsum ax bx),(fsum ay by),(fsum az bz))

 fun
diff(VEC(ax,ay,az),VEC(bx,by,bz))=VEC((fdiff ax bx),(fdiff ay by),(fdiff az bz))
                                                                            
fun 
dot(VEC(ax,ay,az),VEC(bx,by,bz))= fsum (fsum (fmult ax bx) (fmult ay by)) (fmult az bz)

fun 
cross(VEC(ax,ay,az),VEC(bx,by,bz))=VEC((fdiff (fmult ay bz) (fmult by 
az)),
				(fdiff (fmult bx az) (fmult ax bz)),
				(fdiff (fmult ax by) (fmult bx ay)))

fun diffr f x = ((f (x +0.0001)) - (f x))/0.0001
fun partx a y1 z1 x1 =let
                fun a1 y z x = a x y z
             in
                diffr ( a1 y1 z1) x1 end
fun party a z1 x1 y1=let
                fun a1 z x y = a x y z
		in
                diffr (a1 x1 z1) y1 end
fun partz a x1 y1 z1 = diffr( a x1 y1 ) z1

fun curl
(VEC(ax,ay,az))=VEC(fdiff (party az) (partz ay),fdiff (partz ax) (partx 
az),fdiff (partx ay) (partz ax))

fun dvg(VEC(ax,ay,az))=(fsum (partx ax) (fsum  (party ay) (partz az)))
end