The ring L.cache.mbRing, see mbRing, is used to get an output of LieElements with indexed basis elements, which sometimes is better to use than the iterated Lie products of generators, especially in high degrees. Use indexFormLie to get the output in L.cache.mbRing and defLie to get back the standard output. The ring L.cache.mbRing is very large, it has as many generators as the total dimension of the computed Lie algebra, so to avoid a large output you should give the ring a name. The composition indexFormLie(defLie x) gives back x, when x is a linear polynomial in L.cache.mbRing. When x is a LieElement in L, the composition defLie(indexFormLie x) is equal to x modulo the relations in L.
i1 : L = lieAlgebra{a,b,c} o1 = L o1 : LieAlgebra |
i2 : x = (basisLie 2)_0 (basisLie 3)_4 o2 = - (a c b b a) + (b a c b a) - (b c a b a) + (c b a b a) o2 : L |
i3 : R = L.cache.mbRing o3 = R o3 : PolynomialRing |
i4 : length gens R o4 = 80 |
i5 : indexFormLie x o5 = mb - mb - mb + mb {5, 5} {5, 7} {5, 12} {5, 15} o5 : R |
i6 : defLie oo o6 = - (a c b b a) + (b a c b a) - (b c a b a) + (c b a b a) o6 : L |
i7 : indexFormLie{c,b c,a b c,a a b c} o7 = {mb , -mb , mb - mb , - mb + 2mb - {1, 2} {2, 2} {3, 2} {3, 4} {4, 2} {4, 5} ------------------------------------------------------------------------ mb } {4, 9} o7 : List |
i8 : defLie oo o8 = {c, - (c b), - (b c a) + (c b a), 2 (a c b a) - (b a c a) - (c a b a)} o8 : List |
i9 : {c,b c,a b c,a a b c} o9 = {c, - (c b), - (b c a) + (c b a), 2 (a c b a) - (b a c a) - (c a b a)} o9 : List |