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# normalForm -- compute the normal form of a LieElement

- 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

## See also

- standardForm(RingElement,LieAlgebra) -- get a Lie element in standard form
- indexForm -- get a Lie element in the polynomial ring representation
- LieElement @ LieElement -- formal multiplication of Lie elements

## Ways to use normalForm:

- `normalForm(LieElement)`

## For the programmer

The object normalForm is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2:1829:0.