Leibniz.jl
Operator algebras for multivariate differentiable Julia expressions
Compatibility of Grassmann.jl for multivariable differential operators and tensor field operations.
julia> using Leibniz, Grassmann
Reduce (Free CSL version, revision 4980), 06-May-19 ...
julia> V = tangent(ℝ^3,4,3)
⟨+++⟩
julia> V(∇)
∂₁v₁ + ∂₂v₂ + ∂₃v₃
julia> V(∇^2)
0 + 1∂₁∂₁ + 1∂₂∂₂ + 1∂₃∂₃
julia> V(∇^3)
0 + 1∂₁∂₁∂₁v₁ + 1∂₂∂₂∂₂v₂ + 1∂₃∂₃∂₃v₃ + 1∂₂∂₁₂v₁ + 1∂₃∂₁₃v₁ + 1∂₁∂₁₂v₂ + 1∂₃∂₂₃v₂ + 1∂₁∂₁₃v₃ + 1∂₂∂₂₃v₃
julia> V(∇^4)
0.0 + 1∂₁∂₁∂₁∂₁ + 1∂₂∂₂∂₂∂₂ + 1∂₃∂₃∂₃∂₃ + 2∂₁₂∂₁₂ + 2∂₁₃∂₁₃ + 2∂₂₃∂₂₃
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.