# normalForm -- compute the normal form of a LieElement

## Synopsis

• Usage:
c = normalForm(x)
• Inputs:
• x, an instance of the type LieElement, $x$ is of type $L$, where $L$ is of type LieAlgebra
• Outputs:
• c, an instance of the type LieElement, the normal form of $x$

## Description

A Lie element obtained as a linear combination of iterated Lie products of generators has an output that is of normal form. If the Lie element is defined by the "formal" operators, then the output may be of non-normal form, and in this case, the normal form is obtained using normalForm.

 i1 : L = lieAlgebra{a,b,c} o1 = L o1 : LieAlgebra i2 : x = a b c - 3 c b a +(1/3) b a c o2 = - (4/3)(b c a) - 2 (c b a) o2 : L i3 : y = a@b@c/3@c@b@a++(1/3)@b@a@c o3 = (a b c) - 3 (c b a) + (1/3)(b a c) o3 : L i4 : normalForm y o4 = - (4/3)(b c a) - 2 (c b a) o4 : L