Lipschitz and Hurwitz quaternions

[chrisvwx]

My understanding is that the current implementation of Quaternions with Int inputs is aligned with the idea of a Lipschitz quaternion.

julia> Quaternion(1,2,3,4)
Quaternion{Int64}(1, 2, 3, 4, false)

On the other hand, in many cases one wants a Hurwitz quaternion. Even though I don't have a clear idea how a Hurwitz quaternion would be integrated with this package, I thought perhaps an issue about it would at least provide a place to discuss the topic.

[chakravala]

i think the obvious solution is to implement another "<:Real" type which stores an integer, but divides it by 2 and prints it, and then use that as coefficients

[chakravala]

Alright, I went ahead and created the https://github.com/chakravala/HalfIntegers.jl package, let me know if you try it.

[chakravala]

Apparently there is another existing repository doing the same thing https://github.com/sostock/HalfIntegers.jl

[hyrodium]

I think this issue is solved with HalfIntegers.jl. It would be nice to have more documentation for Hurwitz quaternions.