# mbRing -- a polynomial ring representation of the Lie algebra used for output

## Synopsis

• Usage:
R=L#cache.mbRing
• Outputs:
• R, ,

## Description

The ring is used as a representation of the Lie algebra $L$ and may be obtained as L#cache.mbRing. The ring mbRing is very large: it has as many generators as the total dimension of the computed Lie algebra. For this reason, you should give the ring a name to avoid a large output. In order to transform a Lie element to a linear polynomial in L#cache.mbRing, use indexForm. For the other direction, use standardForm(RingElement,LieAlgebra).

 i1 : L=lieAlgebra{a,b,c}/{a b-a c} o1 = L o1 : LieAlgebra i2 : dims(1,5,L) o2 = {3, 2, 5, 10, 24} o2 : List i3 : R=L#cache.mbRing o3 = R o3 : PolynomialRing i4 : numgens R o4 = 44 i5 : indexForm(a a a a b+a a a b c) o5 = - mb - mb + mb {5, 0} {5, 1} {5, 2} o5 : R i6 : standardForm(oo,L) o6 = - (a a a c a) - (b a a c a) + (c a a c a) o6 : L i7 : a a a a b+a a a b c o7 = - (a a a c a) - (b a a c a) + (c a a c a) o7 : L