generate rotation quaternions using exp

[karlwessel]

I wanted to do a test your package by implementing Quaternions and tried to create a quaternion q for a rotation around a vector v = (a, b, c) by an angle alpha using exponentials:
q = exp(alpha/2*(ai + bj + ck))

However the exponential function doesn't seem to be fully implemented yet for multivectors? At least i get an error in the following MWE:

julia> using Grassmann

julia> i, j, k = hyperplanes(ℝ^3)
3-element Array{SValue{⟨+++⟩,2,B,Int64} where B,1}:
 -1v₂₃
 1v₁₃ 
 -1v₁₂

julia> alpha = 0.5π
1.5707963267948966

julia> exp(alpha/2*(i))
0.7071067811865476 - 0.7071067811865475v₂₃

julia> a, b, c = 1/sqrt(2) * [1, 1, 0]
3-element Array{Float64,1}:
 0.7071067811865475
 0.7071067811865475
 0.0               

julia> exp(alpha/2*(a*i + b*j + c*k))
ERROR: MethodError: no method matching abs(::StaticArrays.MArray{Tuple{8},Float64,1,8})
Closest candidates are:
  abs(::Bool) at bool.jl:91
  abs(::Float16) at float.jl:520
  abs(::Float32) at float.jl:521
  ...
Stacktrace:
 [1] abs(::MultiVector{Float64,⟨+++⟩,8}) at .julia/packages/AbstractTensors/fUnNY/src/AbstractTensors.jl:55
 [2] _broadcast_getindex_evalf at ./broadcast.jl:578 [inlined]
 [3] _broadcast_getindex at ./broadcast.jl:551 [inlined]
 [4] getindex at ./broadcast.jl:511 [inlined]
 [5] copyto_nonleaf!(::Array{Float64,1}, ::Base.Broadcast.Broadcasted{Base.Broadcast.DefaultArrayStyle{1},Tuple{Base.OneTo{Int64}},typeof(abs),Tuple{Base.Broadcast.Extruded{Array{TensorAlgebra{⟨+++⟩},1},Tuple{Bool},Tuple{Int64}}}}, ::Base.OneTo{Int64}, ::Int64, ::Int64) at ./broadcast.jl:928
 [6] copy at ./broadcast.jl:791 [inlined]
 [7] materialize at ./broadcast.jl:753 [inlined]
 [8] exp(::SBlade{Float64,⟨+++⟩,2,3}) at .julia/packages/Grassmann/wWv7E/src/algebra.jl:961
 [9] top-level scope at none:0

[chakravala]

Thanks for opening the issue. The algorithm for the exp method is a rough draft at the moment and I have received some feedback about how to improve it, but have not followed through on it yet.

[karlwessel]

Thank you for the quick response! Then i'll just fall back to sine and cosine to create the quaternion for now.

[chakravala]

That exp call should work now

julia> exp(alpha/2*(a*i + b*j + c*k))
0.7071067811865476 + 0.5v₁₃ - 0.5v₂₃

julia> ans == (sqrt(2)+j+i)/2
true