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Question: RE: LieDerivative

Question:RE: LieDerivative

pik1432 245 Maple 2022
liederivative differentialgeometry
March 07 2023
0

Hello there, 

Is there any chance to ask this one question?

The attached (following) worksheet shows the result of LieDerivative operation, which is not correct. 

The correct answer is given in the image in the middle of the worksheet. Is there any particular reason regarding Maple's way of conducting the operation in that way?

> 

restart;
> 

with(LinearAlgebra):
> 

with(DifferentialGeometry):
> 

with(LieAlgebras):
> 

DGsetup([x1, x2], M, verbose);

`The following coordinates have been protected:`

  

[x1, x2]

  

`The following vector fields have been defined and protected:`

  

[_DG([["vector", M, []], [[[1], 1]]]), _DG([["vector", M, []], [[[2], 1]]])]

  

`The following differential 1-forms have been defined and protected:`

  

[_DG([["form", M, 1], [[[1], 1]]]), _DG([["form", M, 1], [[[2], 1]]])]

  

`frame name: M`

 (1)
> 

 

M > 

f := evalDG((x2)*D_x1 + (c1 * (1 - x1^2) * x2 - c2 * x1)*D_x2);

_DG([["vector", M, []], [[[1], x2], [[2], -c1*x1^2*x2+c1*x2-c2*x1]]])

 (2)
M > 

h := evalDG((x1)*D_x1 + (0)*D_x2);

_DG([["vector", M, []], [[[1], x1]]])

 (3)
M > 

###### answer
M > 

M > 

LieDerivative(f, h);

_DG([["vector", M, []], [[[1], x2], [[2], x1*(2*c1*x1*x2+c2)]]])

 (4)
M > 

 

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