# LieAlgebra ++ LieAlgebra -- direct sum of Lie algebras

## Synopsis

• Operator: ++
• Usage:
S = L++M
• Inputs:
• Outputs:
• S, an instance of the type LieAlgebra, the direct sum of $L$ and $M$

## Description

 i1 : F1 = lieAlgebra({a,b},Signs=>{0,1},Weights=>{{2,0},{2,1}}, LastWeightHomological=>true) o1 = F1 o1 : LieAlgebra i2 : L1 = differentialLieAlgebra{0_F1,a} o2 = L1 o2 : LieAlgebra i3 : F2 = lieAlgebra({a,b,c},Weights=>{{1,0},{2,1},{3,2}}, Signs=>{1,1,1},LastWeightHomological=>true) o3 = F2 o3 : LieAlgebra i4 : L2 = differentialLieAlgebra{0_F2,a a,a b}/{b b+4 a c} o4 = L2 o4 : LieAlgebra i5 : T=L1++L2 o5 = T o5 : LieAlgebra i6 : describe(T) o6 = generators => {pr , pr , pr , pr , pr } 0 1 2 3 4 Weights => {{2, 0}, {2, 1}, {1, 0}, {2, 1}, {3, 2}} Signs => {0, 1, 1, 1, 1} ideal => { - (pr_2 pr_2 pr_2), (pr_3 pr_3) + 4 (pr_2 pr_4), (pr_2 pr_2 pr_3) + (pr_2 pr_2 pr_3) - (pr_3 pr_2 pr_2) - 4 (pr_2 pr_2 pr_3), (pr_0 pr_2), (pr_0 pr_3), (pr_0 pr_4), (pr_1 pr_2), (pr_1 pr_3), (pr_1 pr_4)} ambient => LieAlgebra{...10...} diff => {0, pr_0, 0, (pr_2 pr_2), (pr_2 pr_3)} Field => QQ computedDegree => 0 i7 : normalForm\ideal(T) o7 = {0, (pr_3 pr_3) + 4 (pr_2 pr_4), 0, - (pr_2 pr_0), - (pr_3 pr_0), ------------------------------------------------------------------------ (pr_0 pr_4), (pr_2 pr_1), (pr_3 pr_1), (pr_1 pr_4)} o7 : List