# lieRing -- get the internal ring for representation of Lie elements

## Synopsis

• Usage:
R = L#cache.lieRing
• Inputs:
• Outputs:
• R, ,

## Description

The ring $R$ is the internal polynomial ring representation of Lie elements, which can be obtained by writing L#cache.lieRing. The Lie monomials are represented as commutative monomials in this ring. The number of generators in lieRing is the number of generators in the Lie algebra times the internal counter L#cache.max, which initially is set to $5$, and is changed to $n+5$ if a computation is performed up to degree $n$ with $n\ >$ L#cache.max.

 i1 : L=lieAlgebra{a,b}/{a a a b,b b b a} o1 = L o1 : LieAlgebra i2 : dims(1,4,L) o2 = {2, 1, 2, 1} o2 : List i3 : L#cache.max o3 = 5 i4 : L#cache.lieRing o4 = QQ[aR ..aR ] 0 9 o4 : PolynomialRing i5 : dims(1,6,L) o5 = {2, 1, 2, 1, 2, 1} o5 : List i6 : L#cache.max o6 = 11 i7 : numgens L#cache.lieRing o7 = 22 i8 : dims(1,10,L) o8 = {2, 1, 2, 1, 2, 1, 2, 1, 2, 1} o8 : List i9 : L#cache.max o9 = 11 i10 : numgens L#cache.lieRing o10 = 22