# Question:Extract term from Lie derivative

## Question:Extract term from Lie derivative

Maple

Hi;

To compute higher-order lie derivatives we need to pass a vector field to LieDerivative(..) function. What follows is the result of LieDerivative(..) command:

To compute 2nd-order lie derivative we should first create a vector field as follows:

L1fh := ((1/2)*(x+u)*(-2*y+2*x)/sqrt((y-x)^2+L^2))*D_x + ((1/2)*(y+v)*(2*y-2*x)/sqrt((y-x)^2+L^2))*D_y + (L^2/sqrt((y-x)^2+L^2))*D_L;

Is there a function to extraxt components of an expression which is the result of the LieDerivative(..)? For example how we can extract the first term. i.e. :

sample code:

with(DifferentialGeometry):

DGsetup([x, y, L], R3);

h := sqrt((y-x)^2 + L^2);

f := evalDG((x+u)*D_x + (y+v)*D_y + L*D_L);

L1fh := LieDerivative(f, h);

simplify(L1fh);

L2fh := LieDerivative(L1fh, h);

L1fh := ((1/2)*(x+u)*(-2*y+2*x)/sqrt((y-x)^2+L^2))*D_x + ((1/2)*(y+v)*(2*y-2*x)/sqrt((y-x)^2+L^2))*D_y + (L^2/sqrt((y-x)^2+L^2))*D_L;

L2fh := LieDerivative(L1fh, h);

simplify(L2fh);

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