differentiable.jl

struct Partial{Order}
    indices::CartesianIndex{Order}
end

function Partial(indices::Integer...)
    return Partial{length(indices)}(CartesianIndex(indices))
end

compact_string_representation(::Partial{0}) = print(io, "id")
function compact_string_representation(p::Partial)
    tuple = Tuple(p.indices)
    lower_numbers = @. (n -> '₀' + n)(reverse(digits(tuple)))
    return join(["∂$(join(x))" for x in lower_numbers])
end
function Base.show(io::IO, ::MIME"text/plain", p::Partial)
    if get(io, :compact, false)
        print(io, "Partial($(Tuple(p.indices)))")
    else
        print(io, compact_string_representation(p))
    end
end

function Base.show(io::IO, ::MIME"text/html", p::Partial)
    tuple = Tuple(p.indices)
    if get(io, :compact, false)
        print(io, join(map(n -> "∂<sub>$(n)</sub>", tuple), ""))
    else
        print(io, compact_string_representation(p))
    end
end