Macaulay2 » Documentation
Packages » GradedLieAlgebras :: mbRing
next | previous | forward | backward | up | index | toc

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

- Usage:
    `R=L#cache.mbRing`
- Outputs:
  - R, a polynomial ring,

## 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

## See also

- indexForm -- get a Lie element in the polynomial ring representation
- standardForm(RingElement,LieAlgebra) -- get a Lie element in standard form
- lieRing -- get the internal ring for representation of Lie elements

## For the programmer

The object mbRing is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc2.m2:1712:0.