The signs of the generators, see genSigns define the sign of an arbitrary expression. The sign of [] is defined to be 0. However, the sign of [] should be thought of as arbitrary since, in the example below, the element [a1,a1,a1] has sign 1 and is still equal to [] in L.
i1 : L = lieAlgebra( {a_1,a_2}, {}, genSigns => {1,0}) o1 = L o1 : LieAlgebra |
i2 : prod=multLie([a_1,a_1],[a_2]) o2 = {{-1}, {[a , a , a ]}} 2 1 1 o2 : List |
i3 : signLie oo o3 = 0 |
i4 : signLie{[a_2],[a_1,a_1,a_1],{{1,2},{[a_1,a_2,a_2],[a_2,a_2,a_1]}}} o4 = {0, 1, 1} o4 : List |
i5 : indexFormLie prod o5 = -mb {3, 0} o5 : QQ[mb , mb , mb , mb , mb , mb ] {1, 0} {1, 1} {2, 0} {2, 1} {3, 0} {3, 1} |
i6 : signLie oo o6 = 0 |