In the example below, ExtUL(QQ,QQ) is equal to R and a basis as a vector space is given by the generators of the ring representation L.cache.extAlgRing, see extAlgRing.
i1 : R=QQ[x,y,z, SkewCommutative=>{x,y,z}]
o1 = R
o1 : PolynomialRing
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i2 : L=koszulDualLie(R) o2 = L o2 : LieAlgebra |
i3 : extAlgLie 3
o3 = | 3 0 0 |
| 0 3 0 |
| 0 0 1 |
3 3
o3 : Matrix ZZ <--- ZZ
|
i4 : L.cache.extAlgRing
o4 = QQ[ext , ext , ext , ext , ext , ext , ext ]
0 1 2 3 4 5 6
o4 : PolynomialRing
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i5 : m=extAlgMultLie(ext_1,ext_2)
o5 = -ext
3
o5 : QQ[ext , ext , ext , ext , ext , ext , ext ]
0 1 2 3 4 5 6
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i6 : extAlgMultLie(ext_0,m)
o6 = ext
6
o6 : QQ[ext , ext , ext , ext , ext , ext , ext ]
0 1 2 3 4 5 6
|