yeah, thank you very much.

you are right, indeed, there is something wrong with my fitting. assume that there are n different points and there coodinate is x[i],y[i],z[i] (i is integer and from 1 to n) respectivly. what I need to do is try to find a function f(x,y), so the sum((f(x[i],y[i])-z[i])^2,i=1..n) get the minimize. To single point, the answer after differentiated may have no meaning.

I use the order as follows:

restart;

eq:=sum((a1*x[i]^2+a2*y[i]^2+a3*x[i]*y[i]+a4*x[i]+a5*y[i]+a6-z[i])^2,i=1..n);

S:=map2(diff,eq,[a1,a2,a3,a4,a5,a6]);

solve(S,{a1,a2,a3,a4,a5,a6});

and I am quite surprised to see that maple get me so long an answer.

thank you again for your help.