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DiffAlgField | DiffAlgField -- Lie bracket

Operator: |
Usage:

X | Y
Inputs:
- X, an instance of the type DiffAlgField, a vector field
- Y, an instance of the type DiffAlgField, a vector field
Outputs:
- an instance of the type DiffAlgField, the Lie bracket of X and Y

Description

This function computes the Lie bracket of two vector fields.

i1 : X = random newField(2,1,"a")

o1 = - x ax  + (- 4x  + 3x  + x )ax  + (- 4x  + x  + 5x )ax
        1  0        0     1    2   1        0    1     2   2

o1 : DiffAlgField

i2 : Y = random newField(2,1,"b")

o2 = (4x  + 7x  + 3x )ax  + (2x  - 3x  + 4x )ax  + (6x  - 2x )ax
        0     1     2   0      0     1     2   1      0     1   2

o2 : DiffAlgField

i3 : X | Y

o3 = (- 38x  + 17x  + 26x )ax  + (32x  + 17x )ax  + (- 8x  + 29x  + 6x )ax
           0      1      2   0       1      2   1        0      1     2   2

o3 : DiffAlgField

See also

isInvolutive -- tests if a distribution is involutive

Ways to use this method:

DiffAlgField | DiffAlgField -- Lie bracket

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DiffAlg.m2:1065:0.