i1 : L = lieAlgebra( {a,b}, {[a,a,a,b]},genWeights => {{1,1},{1,2}},
genSigns=>{1,0})
o1 = L
o1 : LieAlgebra
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i2 : b2 = basisLie 2
o2 = {[a, a], [b, a]}
o2 : List
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i3 : b3 = basisLie 3
o3 = {[b, a, a], [b, b, a]}
o3 : List
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i4 : multListLie(b2,b3)
1 1
o4 = {[], {{-1}, {[a, b, b, a, a]}}, {{-1}, {[a, b, b, a, a]}}, {{- -, -},
2 4
------------------------------------------------------------------------
{[b, a, b, b, a], [b, b, b, a, a]}}}
o4 : List
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i5 : indexFormLie oo
1 1
o5 = {0, -mb , -mb , -mb - -mb }
{5, 0} {5, 0} 4 {5, 1} 2 {5, 2}
o5 : List
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There is an option multOnly which only multiplies those pairs (x,y) for which multOnly(x,y) is true.
i6 :
apply(b2,weightLie)
o6 = {{2, 2, 0}, {2, 3, 0}}
o6 : List
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i7 : apply(b3,weightLie)
o7 = {{3, 4, 0}, {3, 5, 0}}
o7 : List
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i8 : multListLie(b2,b3,multOnly=>(x,y)->
(weightLie x)_1 === 3 and (weightLie y)_1 === 5)
1 1
o8 = {{{- -, -}, {[b, a, b, b, a], [b, b, b, a, a]}}}
2 4
o8 : List
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i9 : indexFormLie oo
1 1
o9 = {-mb - -mb }
4 {5, 1} 2 {5, 2}
o9 : List
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