lie -- lie bracket of two elements

Usage:

c = lie(a, b)
Inputs:
- a, an instance of the type NCRingElement,
- b, an instance of the type NCRingElement,
Outputs:
- c, an instance of the type NCRingElement, The commutator of a, b;

Description

A non-commutative algebra $(R, +, \cdot)$ is naturally a Lie algebra with the commutator $a\cdot b - b\cdot a$ as the Lie bracket. The commutator of two non-commutative polynomials can be computed as follows:

i1 : R = wordAlgebra (3);

i2 : a = [1]_R

o2 = Lt
       1

o2 : R

i3 : b = [2]_R

o3 = Lt
       2

o3 : R

i4 : lie(a,b)

o4 = -Lt Lt +Lt Lt
        2  1   1  2

o4 : R

For the programmer

The object lie is a function closure.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PathSignatures/documentation.m2:918:0.