If the Lie algebra has no differential, the program adds an extra last homological degree zero to each generator. The weight of [] is defined to be a list of zeroes of the same length as the weight of the generators. However, the weight of [] should be thought of as arbitrary since, in the example below, the element [b,b] has weight 2,2,0 and is equal to [] in L.
i1 : L=lieAlgebra({a,b,c},{},genWeights => {{1,1},{1,1},{2,2}})
o1 = L
o1 : LieAlgebra
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i2 : weightLie(a)
o2 = {1, 1, 0}
o2 : List
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i3 : weightLie([a,a,b,a])
o3 = {4, 4, 0}
o3 : List
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i4 : g={{1,-1},{[a,c],[b,c]}}
o4 = {{1, -1}, {[a, c], [b, c]}}
o4 : List
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i5 : weightLie g
o5 = {3, 3, 0}
o5 : List
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i6 : m=indexFormLie g
o6 = mb - mb
{3, 2} {3, 3}
o6 : QQ[mb , mb , mb , mb , mb , mb , mb , mb ]
{1, 0} {1, 1} {2, 0} {2, 1} {3, 0} {3, 1} {3, 2} {3, 3}
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i7 : degree m
o7 = {3, 3, 0}
o7 : List
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i8 : weightLie{[],[b,b],{{1,2},{[c],[a,b]}}}
o8 = {{0, 0, 0}, {2, 2, 0}, {2, 2, 0}}
o8 : List
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It is possible to use weightLie also in the case when the generators are indexedVariables or integers.
i9 : L2=lieAlgebra({a_2,b,1},{}, genWeights => {1,2,3})
o9 = L2
o9 : LieAlgebra
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i10 : weightLie(1)
o10 = {3, 0}
o10 : List
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