Jacobian using in Maple

Question

How can I use the Jacobian written below as function from (x, y) ?

g := (x, y) -> x - y
u := (x, y) -> x^2 + y^2

J := jacobian([g(x, y), u(x, y)], [x, y]);

My idea was to make funcion like this

Jf := (u, v) -> subs(x = u, y = v, J(x, y))

but it returns ugly matrix with brakets inside.

P. S. I use Maple 17

Answer 1

The linalg package (which exports the jacobian command) and lowercase matrix are deprecated. Use LinearAlgebra and Matrix instead, and VectorCalculus:-Jacobian.

Also, note the use of unapply.

restart:

g := (x, y) -> x - y:

u := (x, y) -> x^2 + y^2:

J:=VectorCalculus:-Jacobian([g(x,y),u(x,y)],[x,y]);

                                [ 1     -1 ]
                           J := [          ]
                                [2 x    2 y]

Jf:=unapply(J,[x,y]):

Jf(1,1);

                               [1    -1]
                               [       ]
                               [2     2]

Jf(s,t);
                             [ 1     -1 ]
                             [          ]
                             [2 s    2 t]