LieGroups provides Lie group objects and their operations.
julia> using LieGroups
julia> θ = 45/180*π
0.7853981633974483
julia> alg = so{2}([θ])
so{2, Vector{Float64}}([0.7853981633974483])
julia> g = exp(∧(alg))
SO{2}(A=[0.7071067811865476 -0.7071067811865475; 0.7071067811865475 0.7071067811865477])
julia> g ⋉ [1, 0]
2-element Vector{Float64}:
0.7071067811865476
0.7071067811865475
julia> (g * g) ⋉ [1, 0]
2-element Vector{Float64}:
2.220446049250313e-16
1.0
julia> alg2 = log(g * g)
so{2, Vector{Float64}}([1.5707963267948966])
julia> alg2 == alg + alg
true