i1 : L = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}},
Signs=>{1,1,1},LastWeightHomological=>true)
o1 = L
o1 : LieAlgebra
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i2 : D= differentialLieAlgebra({0_L,a a,a b})
o2 = D
o2 : LieAlgebra
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i3 : J=lieIdeal({b b + 4 a c})
o3 = J
o3 : FGLieIdeal
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i4 : Q=D/J
o4 = Q
o4 : LieAlgebra
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i5 : dims(7,Q)
o5 = | 1 1 0 0 0 0 0 |
| 0 1 1 1 1 1 1 |
| 0 0 1 1 1 1 2 |
| 0 0 0 0 1 1 2 |
| 0 0 0 0 0 1 1 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
7 7
o5 : Matrix ZZ <--- ZZ
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i6 : Z=cycles Q
o6 = Z
o6 : LieSubAlgebra
|
i7 : dims(5,Z)
o7 = | 1 1 0 0 0 |
| 0 0 1 1 1 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
5 5
o7 : Matrix ZZ <--- ZZ
|
i8 : H=lieHomology Q
o8 = H
o8 : VectorSpace
|
i9 : dims(1,5,H)
o9 = {1, 0, 0, 0, 1}
o9 : List
|
i10 : E=extAlgebra(5,Q)
o10 = E
o10 : ExtAlgebra
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i11 : dims(4,E)
o11 = | 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
4 4
o11 : Matrix ZZ <--- ZZ
|