Compatibility with Unitful Quantity types

[mikeingold]

Following up from #25, I would love to be able to use this package with Unitful.Quantity types. The following MWE demonstrates a usage that I would like to have work, but that currently doesn't.

using CliffordNumbers: KVector, VGA, ∧
using LinearAlgebra: norm
using Unitful

a = KVector{1, VGA(3)}(1.0u"m", 0.0u"m", 0.0u"m")
b = KVector{1, VGA(3)}(0.0u"m", 2.0u"m", 0.0u"m")
c = KVector{1, VGA(3)}(0.0u"m", 0.0u"m", 3.0u"m")

norm(a ∧ b ∧ c)
# -> 6.0u"m^3"

[brainandforce]

One thing I'll note here is the restriction of the scalars of AbstractCliffordNumber subtypes to Union{Real,Complex}. This is very much intentional: it would be a bad idea to use a Quaternion or an AbstractCliffordNumber as the scalar field when Clifford algebras are restricted to real or complex scalars. Unitful.Quantity does not subtype Real or Complex so it cannot be used as an element type for an AbstractCliffordNumber.

To get around this, you can just wrap a KVector or other AbstractCliffordNumber directly in a Quantity, since any subtype of Number is allowed to be wrapped:

julia> using CliffordNumbers, Unitful

julia> KVector{1,VGA(3)}(1, 2, 3)u"m"
3-element KVector{1, VGA(3), Int64}:
1e₁ + 2e₂ + 3e₃ m

julia> typeof(ans)
Quantity{KVector{1, VGA(3), Int64, 3}, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}

(There is a printing issue here since Base.show(::IO, ::Quantity) calls Base.show(::IO, ::AbstractCliffordNumber), which then calls Base.summary(::IO, ::AbstractCliffordNumber), so the summary for the wrapped type is printed instead of the one for the type itself.)

[brainandforce]

I still need to include support for a few other operations, but your use case should be covered by this initial package extension.

[mikeingold]

Thanks! I’m looking forward to trying it out.

[brainandforce]

Final update: this has been released as of 0.1.9.