@Kitonum Excellent, thank you very much.

@Carl Love Thank you for answer. When f is a vector field, for exapmle f:=[x_1, 0, 1], now how we can compute its Jacobian?

diff~(f, x);

does not return a Jacobian matrix.

@Rouben Rostamian  

Merci for answer. That sounds great; since there is no longer need to define a VectorField object. But the question of @tomleslie is still remains open.

@tomleslie Thank you for answer. There was a typo in my question. Sorry for that.

@Carl Love Merci beaucoup.

@Carl Love Thank you for reply. Yes, we can use coeff(..) as well as GetComponents(..) to extract terms from the second form of the L1fh above.

But my question is how we can extract terms from the following expression (without D_x, D_y, and D_L):

PS:

In Python's Sympy package we can simply use ".args" attribute: L1fh.args or L1fh.args[0]

@Torre Thank you very much.

@Carl Love 

You're right. Thank you.

@Carl Love 

Thank you so much.

@Carl Love 

Thanks that works.

For example, please consider the Maple codes below:

Plex:=[x,y,z];
f1:= x*y-z^2+2*x;
f2:=x^3-2*y^2+z;
f3:=x-y+4*z;
Polys:=[f1,f2,f3];
F:=Polys;
with(MTM):
n:=size(Plex,2)-1;

for i from 1 to n do  
S||i:=resultant(F[i],F[i+1],Plex[1])
od;

So, the question is how can I implement Matlab's "while" loop in Maple?