The optional input given above is not relevant for Lie algebras. A minimal set of generators and relations for the Lie algebra $L$ (without differential) is given. In general the presentation applies to $H_0(L)$. The example $L$ below is the Lie algebra of strictly upper triangular $4\times 4$-matrices given by its multiplication table on the natural basis.
i1 : L=lieAlgebra({e12,e23,e34,e13,e24,e14},Weights=>{1,1,1,2,2,3})/
{e12 e34,e12 e13,e12 e14,
e23 e13,e23 e24,e23 e14,
e34 e24,e34 e14,e13 e24,
e13 e14,e24 e14,
e12 e23 - e13,
e12 e24 - e14,
e13 e34 - e14,
e23 e34 - e24}
o1 = L
o1 : LieAlgebra
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i2 : M=minimalPresentation(3,L) o2 = M o2 : LieAlgebra |
i3 : describe M
o3 = generators => {e12, e23, e34}
Weights => {{1, 0}, {1, 0}, {1, 0}}
Signs => {0, 0, 0}
ideal => {(e34 e12), (e34 e34 e23), (e23 e34 e23), (e23 e23 e12), (e12 e23 e12)}
ambient => LieAlgebra{...10...}
diff => {}
Field => QQ
computedDegree => 0
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i4 : dims(1,4,M)
o4 = {3, 2, 1, 0}
o4 : List
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