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

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

Synopsis

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

For the programmer

The object mbRing is a symbol.