A basis is given in the specified degree or multidegree. Observe that if the Lie algebra has no differential, then an extra homological degree=0 is added to the given weights of the generators.
i1 : L = lieAlgebra({a,b,c},{[c,a]},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}})
o1 = L
o1 : LieAlgebra
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i2 : computeLie 4
o2 = {3, 4, 5, 12}
o2 : List
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i3 : d=defLie (mb_{4,5}+2*mb_{4,6})
o3 = {{1, 2}, {[c, b, b, a], [b, c, b, a]}}
o3 : List
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i4 : i=idealBasisLie(5,{[a,a],d})
o4 = {[c, c, b, a, a], {{2, 1}, {[c, b, c, b, a], [c, c, b, b, a]}}, [c, b,
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b, a, a], [c, a, b, b, a], [c, a, b, a, a], [b, c, b, a, a], {{2, 1},
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{[b, b, c, b, a], [b, c, b, b, a]}}, [b, b, b, a, a], [b, a, b, a, a],
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[a, b, b, a, a], [a, a, b, a, a]}
o4 : List
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i5 : length oo o5 = 11 |
i6 : idealLie(5,{[a,a],d})
o6 = {0, 1, 1, 4, 11}
o6 : List
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i7 : weightLie i
o7 = {{5, 4, 0}, {5, 4, 0}, {5, 2, 0}, {5, 2, 0}, {5, 2, 0}, {5, 2, 0}, {5,
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2, 0}, {5, 0, 0}, {5, 0, 0}, {5, 0, 0}, {5, 0, 0}}
o7 : List
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i8 : idealBasisLie({5,4,0},{[a,a],d})
o8 = {[c, c, b, a, a], {{2, 1}, {[c, b, c, b, a], [c, c, b, b, a]}}}
o8 : List
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i9 : indexFormLie oo
o9 = {mb , mb + 2mb }
{5, 7} {5, 13} {5, 15}
o9 : List
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i10 : indexFormLie i
o10 = {mb , mb + 2mb , mb , mb , mb , mb
{5, 7} {5, 13} {5, 15} {5, 5} {5, 9} {5, 2} {5,
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, mb + 2mb , mb , mb , mb , mb }
6} {5, 12} {5, 14} {5, 4} {5, 1} {5, 3} {5, 0}
o10 : List
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