The set of linear polynomials in L.cache.mbRing, see mbRing, gives a representation of the elements in the Lie algebra L. The function defLie gives back the standard output and indexFormLie goes in the other direction.
i1 : L = lieAlgebra{a,b} o1 = L o1 : LieAlgebra |
i2 : b3 = basisLie 3 o2 = {(a b a), (b b a)} o2 : List |
i3 : Q = L.cache.mbRing o3 = Q o3 : PolynomialRing |
i4 : gens Q o4 = {mb , mb , mb , mb , mb } {1, 0} {1, 1} {2, 0} {3, 0} {3, 1} o4 : List |
i5 : c3 = indexFormLie b3 o5 = {mb , mb } {3, 0} {3, 1} o5 : List |
i6 : defLie indexFormLie a a b o6 = - (a b a) o6 : L |
i7 : defLie mb_{3,0} o7 = (a b a) o7 : L |
i8 : defLie (mb_{3,0}+2*mb_{3,1}) o8 = (a b a) + 2 (b b a) o8 : L |
i9 : indexFormLie oo o9 = mb + 2mb {3, 0} {3, 1} o9 : Q |