LieBracket
calculate the Lie bracket of two VectorField objects
Commutator
a synonym for LieBracket
Calling Sequence
Parameters
Description
Examples
Compatibility
LieBracket (X, Y)
Commutator (X, Y)
X
-
a VectorField object
Y
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 Zf=XYf−YXf 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.
withLieAlgebrasOfVectorFields:
U≔VectorFieldxDx+yDy,space=x,y
U≔xⅆⅆx+yⅆⅆy
Tx≔VectorFieldDx,space=x,y
Tx≔ⅆⅆx
LieBracketU,Tx
−ⅆⅆx
which is the same as
CommutatorU,Tx
The LieBracket and Commutator commands were introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
See Also
VectorField (Object overview)
LieAlgebrasOfVectorFields[VectorField]
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