> restart;

> read "C:/books/ess/programs/jacobian.mpl";

> f := [ sin(x-y), cos(x) ];

> J := Jacobian( f, [x,y] );

> stopat( Jacobian );

> showstat( Jacobian );

Jacobian := proc(fnlist::list, varlist::list(name))

local J, i, j, m, n, tmp, inds;

   1*  m := nops(fnlist);

   2   n := nops(varlist);

   3   J := Matrix(m,n,storage = sparse);

   4   for i to m do

   5     inds := indets(fnlist[i]);

   6     for j to n do

   7       if member(varlist[j],inds) then

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

   9         if not Testzero(tmp) then

  10           J[i,j] := tmp

             end if

           end if

         end do

       end do;

  11   J

end proc

> J := Jacobian( f, [x,y] );

Jacobian:

   1*  m := nops(fnlist);

DBG> next

2

Jacobian:

   2   n := nops(varlist);

DBG> next

2

Jacobian:

   3   J := Matrix(m,n,storage = sparse);

DBG> next

Matrix(2, 2, [[0,0],[0,0]], datatype = anything, 

storage = sparse, order = Fortran_order, shape = [])

Jacobian:

   4   for i to m do

         ...

       end do;

DBG> into

Matrix(2, 2, [[0,0],[0,0]], datatype = anything, 

storage = sparse, order = Fortran_order, shape = [])

Jacobian:

   5     inds := indets(fnlist[i]);

DBG> next

{x, y, sin(x-y)}

Jacobian:

   6     for j to n do

           ...

         end do

DBG> list

Jacobian := proc(fnlist::list, varlist::list(name))

local J, i, j, m, n, tmp, inds;

   1*  m := nops(fnlist);

   2   n := nops(varlist);

   3   J := Matrix(m,n,storage = sparse);

   4   for i to m do

   5     inds := indets(fnlist[i]);

   6 !   for j to n do

   7       if member(varlist[j],inds) then

             ...

           end if

           ...

         end do

         ...

       end do;

       ...

end proc

DBG> into

{x, y, sin(x-y)}

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> fnlist[i];

sin(x-y)

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> varlist[i];

x

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> varlist[j];

x

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> into

{x, y, sin(x-y)}

Jacobian:

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

DBG> next

cos(x-y)

Jacobian:

   9         if not Testzero(tmp) then

               ...

             end if

DBG> next

cos(x-y)

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> outfrom

cos(x-y)

Jacobian:

   5     inds := indets(fnlist[i]);

DBG> list

Jacobian := proc(fnlist::list, varlist::list(name))

local J, i, j, m, n, tmp, inds;

   1*  m := nops(fnlist);

   2   n := nops(varlist);

   3   J := Matrix(m,n,storage = sparse);

   4   for i to m do

   5 !   inds := indets(fnlist[i]);

   6     for j to n do

           ...

         end do

         ...

       end do;

       ...

end proc

DBG> i;

2

Jacobian:

   5     inds := indets(fnlist[i]);

DBG> j;

3

Jacobian:

   5     inds := indets(fnlist[i]);

DBG> into

{x, cos(x)}

Jacobian:

   6     for j to n do

           ...

         end do

DBG> into

{x, cos(x)}

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> into

{x, cos(x)}

Jacobian:

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

DBG> i;

2

Jacobian:

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

DBG> j;

1

Jacobian:

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

DBG> into

0

Jacobian:

   9         if not Testzero(tmp) then

               ...

             end if

DBG> outfrom

0

Jacobian:

   7       if member(varlist[j],inds) then

             ...

           end if

DBG> list

Jacobian := proc(fnlist::list, varlist::list(name))

local J, i, j, m, n, tmp, inds;

       ...

   2   n := nops(varlist);

   3   J := Matrix(m,n,storage = sparse);

   4   for i to m do

   5     inds := indets(fnlist[i]);

   6     for j to n do

   7 !     if member(varlist[j],inds) then

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

             ...

           end if

           ...

         end do

         ...

       end do;

       ...

end proc

DBG> outfrom

0

Jacobian:

  11   J

DBG> list

Jacobian := proc(fnlist::list, varlist::list(name))

local J, i, j, m, n, tmp, inds;

       ...

   6     for j to n do

   7       if member(varlist[j],inds) then

   8         tmp := Normalizer(diff(fnlist[i],varlist[i]));

   9         if not Testzero(tmp) then

  10           J[i,j] := tmp

             end if

           end if

         end do

       end do;

  11 ! J

end proc

DBG> cont