Use macros with custom types

Use your own types in geometric algebra expressions

Inputs

If the type you use supports indexing, e.g. Vector, it already works:

using SymbolicGA

x = rand(3)
y = rand(3)

@ga 3 x::1 ∧ y::1

Bivector{Float64, 3, 3}(0.500258629818007, 0.5357843847349241, 0.0008175000041409294)

If your type does not support indexing, and you don't want it to, overload SymbolicGA.getcomponent(::T, [i::Int, [j::Int]]):

struct MyInputType{T}
  values::Vector{T}
end

SymbolicGA.getcomponent(x::MyInputType, i::Int) = x.values[i]

x = MyInputType(rand(3))
y = MyInputType(rand(3))

@ga 3 x::1 ∧ y::1

Bivector{Float64, 3, 3}(-0.2138652569661575, -0.20549721942467916, -0.3651673999054662)

For scalars and aggregates of objects with multiple grades, you will need to overload SymbolicGA.getcomponent(::T) and SymbolicGA.getcomponent(::T, j::Int, i::Int) respectively (see SymbolicGA.getcomponent).

Outputs

If you want to reconstruct a custom type from components, either define a constructor for a single tuple argument, e.g. T(components::Tuple)

struct MyOutputType{T}
  values::Vector{T}
end

MyOutputType(x::Tuple) = MyOutputType(collect(x))

x = rand(3)
y = rand(3)

@ga 3 MyOutputType dual(x::1 ∧ y::1)

Main.MyOutputType{Float64}([0.3266951213977226, -0.21724971388568257, -0.06799243644984554])

If you don't want such constructor to be defined, you can overload SymbolicGA.construct(::Type{T}, ::Tuple) directly:

struct MyOutputType2{T}
  values::Vector{T}
end

SymbolicGA.construct(T::Type{<:MyOutputType2}, x::Tuple) = MyOutputType2(collect(x))

x = rand(3)
y = rand(3)

@ga 3 MyOutputType2 dual(x::1 ∧ y::1)

Main.MyOutputType2{Float64}([0.14218485871355147, 0.11017877817638946, -0.3285963732843947])

Integrations for Vector, Tuple and <:Real have already been defined:

@ga 3 Tuple dual(x::1 ∧ y::1)

(0.14218485871355147, 0.11017877817638946, -0.3285963732843947)

@ga 3 Vector dual(x::1 ∧ y::1)

3-element Vector{Float64}:
  0.14218485871355147
  0.11017877817638946
 -0.3285963732843947

z = rand(3)
@ga 3 Float16 dual(x::1 ∧ y::1 ∧ z::1)

Float16(0.05515)

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