# DiffAlgField | DiffAlgField -- Lie bracket

## Synopsis

• Operator: |
• Usage:
X | Y
• Inputs:
• 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