BeginPackage["Gibbs`"]
                
                (**  Vector Cross Product  **)
                
Cross::usage = 
        "Cross[vec1, vec2] gives the vector product of the 3-vectors
        vec1 and vec2."

Begin["LinearAlgebra`CrossProduct`private`"]

Cross[v1_?VectorQ, v2_?VectorQ] :=
        Module[{m=Minors[{v1,v2},2][[1]]},
                {m[[3]], -m[[2]], m[[1]]}
        ]       /; Length[v1]==Length[v2]==3

(* Properties of cross products. *)

Cross/: Cross[a_,b_]^2 := a.a b.b - (a.b)^2

Cross[a_,a_] = 0

Cross[a_ + b_, c_] := Cross[a,c] + Cross[b,c]
Cross[a_, b_ + c_] := Cross[a,b] + Cross[a,c]

Cross[a_,0] = 0
Cross[0,a_] = 0
Cross[{0,0,0},a_] ={0,0,0}
Cross[a_,{0,0,0}] ={0,0,0}  
Cross[(n_?NumberQ) a_, b_] := n Cross[a, b]

Cross[a_, (n_?NumberQ) b_] := n Cross[a, b]

Cross[a_,Cross[b_,c_]] := (a.c) b - (a.b) c
Cross[Cross[a_,b_],c_] := (a.c) b - (b.c) a

Unprotect[Dot]

(* Properties of dot products. *)

a_ . ((n_?NumberQ) b_) := n (a.b)
((n_?NumberQ) a_) . b_ := n (a.b)

a_ . (b_ + c_) := a.b + a.c
(a_ + b_) . c_ := a.c + b.c

a_ . b_ := b . a  /; !OrderedQ[{a,b}]
Dot[a_,0] = 0
Dot[0,a_] = 0
Dot[{0,0,0},a_] =0
Dot[a_,{0,0,0}] =0  


(*   a_ . {0,0,0} = 0
{0,0,0} . a_ = 0 *)

a_ . Cross[a_,b_] = 0
a_ . Cross[b_,a_] = 0

Cross[a_,b_] . a_ = 0
Cross[b_,a_] . b_ = 0

Cross[a_,b_] . c_ := a . Cross[b,c]

a_ . Cross[b_,c_] := b . Cross[c,a] /; !OrderedQ[{a,b}]
a_ . Cross[b_,c_] := c . Cross[a,b] /; !OrderedQ[{a,c}]

(* This rule must be given after other rules involving Cross
are defined. *)

Cross[a_,b_] := -Cross[b,a] /; !OrderedQ[{a,b}] 




End[]  (* LinearAlgebra`CrossProduct`Private` *)

Protect[Cross,Dot]

EndPackage[ ]  (* LinearAlgebra`CrossProduct` *)

(*:Limitations: none known. *)


(*:Examples:
Cross[ { a, b, c }, { d, e, f } ]

Cross[ { a, b, c }, Cross[ { d, e, f }, { g, h, i } ] ]

*)

Curl[{v1_,v2_,v3_}]:= { D[v3,y]-D[v2,z],
     D[v1,z]-D[v3,x], D[v2,x]-D[v1,y] }

Div[{v1_,v2_,v3_}]:= D[v1,x]+D[v2,y]+D[v3,z]

Grad[s_]:= {D[s,x], D[s,y], D[s,z]} /. {0,0,0}->grad[s]
Grad[a_?NumberQ]:=0
Curl[Grad[s_]]:=0
Curl[grad[s_]]:=0
Div[Curl[s_]]:=0
Curl[-Grad[s_]]:=0
Curl[-grad[s_]]:=0
Div[-Curl[s_]]:=0
Grad[0]=0
Curl[0]=0
Div[0]=0
Grad[a_+b_]:=Grad[a]+Grad[b]
Curl[a_+b_]:=Curl[a]+Curl[b]
Div[a_+b_]:=Div[a]+Div[b]
grad[a_+b_]:=grad[a]+grad[b]