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TableĀ 2 Commutator table after optimization

From: Lie symmetry analysis and invariant solutions of 3D Euler equations for axisymmetric, incompressible, and inviscid flow in the cylindrical coordinates

\([ \boldsymbol{V}_{\boldsymbol{1}}, \boldsymbol{V}_{\boldsymbol{2}}]\) \(\boldsymbol{X}_{\boldsymbol{1}}\) \(\boldsymbol{X}_{\boldsymbol{2}}\) \(\boldsymbol{X}_{\boldsymbol{3}}\) \(\boldsymbol{X}_{\boldsymbol{4}}\)
\(\boldsymbol{X}_{\boldsymbol{1}}\) 0 0 \(\boldsymbol{X}_{\boldsymbol{1}}\) 0
\(\boldsymbol{X}_{\boldsymbol{2}}\) 0 0 \(-2 \boldsymbol{X}_{\boldsymbol{2}}\) \(4 \boldsymbol{X}_{\boldsymbol{2}}\)
\(\boldsymbol{X}_{\boldsymbol{3}}\) \(- \boldsymbol{X}_{\boldsymbol{1}}\) \(2 \boldsymbol{X}_{\boldsymbol{2}}\) 0 0
\(\boldsymbol{X}_{\boldsymbol{4}}\) 0 \(-4 \boldsymbol{X}_{\boldsymbol{2}}\) 0 0