calculate the Lie bracket of two VectorField objects
a synonym for LieBracket
LieBracket (X, Y)
Commutator (X, Y)
a VectorField object
a VectorField object on the same space as X
The Lie bracket of two vector fields X, Y, defined on the same space, is the vector field Z such that Z⁡f=X⁡Y⁡f−Y⁡X⁡f where f is a real-valued function on the same space as X and Y. The standard notation is Z=X,Y.
The LieBracket(X,Y) method returns a VectorField object on the same space as X and Y.
The Commutator method is provided as an alias.
This method is associated with the VectorField object. For more detail, see Overview of the VectorField object.
U ≔ VectorField⁡x⁢Dx+y⁢Dy,space=x,y
Tx ≔ VectorField⁡Dx,space=x,y
which is the same as
The LieBracket and Commutator commands were introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
VectorField (Object overview)
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