The ring representation of the Lie algebra L may be obtained as L.cache.mbRing. Its generators constitute a basis for L up to the computed degree. In order to transform a LieElement to a linear polynomial in L.cache.mbRing, use indexFormLie. For the other direction, use defLie.
i1 : L=lieAlgebra{a,b,c}/{a b-a c} o1 = L o1 : LieAlgebra |
i2 : dimsLie 3 o2 = {3, 2, 5} o2 : List |
i3 : R=L.cache.mbRing o3 = R o3 : PolynomialRing |
i4 : numgens R o4 = 10 |
i5 : indexFormLie(a a b+a a c) o5 = -2mb {3, 0} o5 : R |
i6 : defLie oo o6 = - 2 (a c a) o6 : L |