> # sfb feb 14, 2002
> # Critical Point Extreme Machine
> cpem:=proc(f)
>   local f_x, f_y, f_xx, f_yy, f_xy, bigD, critical, dd, xx, i;
>   f_x:=diff(f,x);f_y:=diff(f,y);
>   f_xx:=diff(f_x,x);f_xy:=diff(f_x,y);f_yy:=diff(f_y,y);
>   bigD:=f_xx*f_yy-(f_xy)^2;
>   critical:=solve({f_x=0,f_y=0},{x,y});
>   for i from 1 to nops([critical]) do
>     if ( nops([critical]) = 1 ) then
>       dd:=eval(bigD,critical); xx:=eval(f_xx,critical);
>     if ( dd < 0 ) then
>       print("The critical point ",critical," is a saddle ", dd,xx);
>     elif ( dd = 0 ) then
>       print("The test fails for ",critical, dd,xx);
>     elif ( xx > 0 ) then
>       print("The critical point ",critical," is a local min ", dd,xx);
>     else
>       print("The critical point ",critical," is a local max ", dd,xx);
>     fi;
>     else
>       dd:=eval(bigD,critical[i]); xx:=eval(f_xx,critical[i]);
>     if ( dd < 0 ) then
>       print("The critical point ",critical[i]," is a saddle ", dd,xx);
>     elif ( dd = 0 ) then
>       print("The test fails for ",critical[i], dd,xx);
>     elif ( xx > 0 ) then
>       print("The critical point ",critical[i]," is a local min ", dd,xx);
>     else
>       print("The critical point ",critical[i]," is a local max ", dd,xx);
>     fi
>     fi;
>   od;
>   #print(f);print(critical);
> end;
> f:=x^2+y^2;cpem(f);
> f:=8*y^3+12*x^2-24*x*y;cpem(f);
> cpem(1-x^2-y^2+x^2*y^2);
> cpem(sin(x)*sin(y));
> f:=x^2*(y+1)^3+y^2;cpem(f);
> solve({diff(1-x^2-y^2+x^2*y^2,x)=0,diff(1-x^2-y^2+x^2*y^2,y)=0},{x,y});
>