Installation

TensND is registered in the Julia General registry.

julia> import Pkg; Pkg.add("TensND")

or, from the Pkg REPL mode (]):

pkg> add TensND

Symbolic backends

What to load for symbolic computations

to work with	add	load
SymPy symbols (Sym: symbols, @syms, SymFunction), and the coordinate systems called without coordinates (coorsys_spherical(), init_cartesian(), …)	pkg> add SymPyPythonCall	using TensND, SymPyPythonCall
Symbolics variables (Num: @variables)	pkg> add Symbolics	using TensND, Symbolics
numbers and derivatives only	nothing	using TensND

Symbolics is a dependency of TensND; SymPyPythonCall is not, since version 0.9.0: what calls Python lives in an extension that loading SymPyPythonCall activates, so that using TensND alone no longer loads Python. Called without coordinates while SymPyPythonCall is not loaded, a coordinate system says so in its error message.

SymPyPythonCall reaches Python through PythonCall, and CondaPkg installs the Python module sympy on first use, in an environment of its own: no Python needs to be set up beforehand. To use a Python of your own instead (one that has sympy), set

ENV["JULIA_CONDAPKG_BACKEND"] = "Null"
ENV["JULIA_PYTHONCALL_EXE"] = "/path/to/python"

before loading SymPyPythonCall.

Code written for SymPy.jl changes using SymPy into using SymPyPythonCall; the symbols of the two packages are different types.

See Symbolic and numeric for how the four scalar worlds — Float64, ForwardDiff.Dual, Sym and Num — relate.

Checking the installation

using TensND

Spherical = coorsys_spherical()
θ, ϕ, r = get_coords(Spherical)
𝐞ᶿ, 𝐞ᵠ, 𝐞ʳ = unitvec(Spherical)
@set_coorsys Spherical

divergence(𝐞ʳ)          # 2/r
laplacian(1 / r)   # 0

If those two return 2/r and 0, the symbolic stack is working.

Citing

@misc{TensND.jl,
  author  = {Jean-François Barthélémy},
  title   = {TensND.jl: symbolic and numerical tensor calculations
             in arbitrary coordinate systems},
  url     = {https://github.com/MicroPoroChemoMechanics/TensND.jl},
  doi     = {10.5281/zenodo.17985768},
  year    = {2026}
}

CITATION.cff in the repository root carries the same metadata in a machine-readable form. Works cited by this documentation are collected on the References page.

Related packages

Package	Role here
Tensors.jl	low-level storage for small tensors
SymPyPythonCall.jl	symbolic backend (SymPy through PythonCall)
Symbolics.jl	native Julia CAS backend
Rotations.jl	rotation representations
ForwardDiff.jl	automatic differentiation