Operator algebras for multivariate differentiable Julia expressions

Cross-compatibility of Grassmann.jl with Reduce.jl for multivariable differential operators and tensor field operations.

julia> using Reduce, Leibniz, Grassmann
Reduce (Free CSL version, revision 4980), 06-May-19 ...

julia> V = V"3" # load Reduce 1st! otherwise slow
⟨+++⟩

julia> V(∇)
∂₁v₁ + ∂₂v₂ + ∂₃v₃

julia> V(∇^0), V(∇^2)
(1v, (∂₁² + ∂₂² + ∂₃²)v)

julia> V(∇^3)
(∂₁³ + ∂₂²∂₁ + ∂₃²∂₁)v₁ + (∂₁²∂₂ + ∂₂³ + ∂₃²∂₂)v₂ + (∂₁²∂₃ + ∂₂²∂₃ + ∂₃³)v₃

julia> V(∇^4)
((∂₁² + ∂₂² + ∂₃²) ^ 2)v

julia> ∇^2 == Δ
true

julia> ∇, Δ
(∂ₖvₖ, ∂ₖ²v)

Generates the tensor algebra of multivariable symmetric Leibniz differentials and interfaces using Reduce, Grassmann to provide the ∇,Δ vector field operators, enabling mixed-symmetry tensors with arbitrary multivariate Grassmann manifolds.

This is an initial undocumented pre-release registration for testing with other packages.