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Tensorial: A Tensor Calculus Package

Renan Cabrera
Organization: University of Windsor
Department: Physics
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Tensorial 3.0: A General Tensor Calculus Package.

The package should be useful both as an introduction to tensor calculations and for advanced calculations. Some of its features are:
  1. There is complete freedom in the choice of symbols for tensor labels and indices.
  2. Base indices may be any set of integers or symbols. Thus you could use {0,1,2,3} for relativity problems, or {t,x,y,z}, or {&rho,&theta,&phi} for spherical coordinates.
  3. Flavored indices (colored or annotated symbols) to represent different coordinate systems.
  4. Tensor shortcuts for easy entry of tensors.
  5. Easy methods to store and substitute tensor values.
  6. Partial, covariant, total, absolute and Lie derivative routines for any dimension and any order.
  7. Complete documentation, with a Help page and numerous examples for each command. In addition there are tutorial and extended example notebooks.
  8. There is an additional package "TMecanica", showing an advanced application of Tensorial for Hamiltonian dynamics.
Tensorial 3.0 can be found at

The notebooks here are an older version, Tensorial 1.3

*Mathematics > Calculus and Analysis > Differential Geometry
*Science > Physics > Relativity Theory

Tensor, Christoffel, RicciThe Metric Tensor, Dummy variables, Kronecker's symbol, Levi-Civita symbol, Christoffel Symbols, Covariant Derivative, Partial Derivative, Divergence Gradient, Laplacian, Absoulte Derivative, Intrinsec Derivative
Related items

*Basic Examples of Relativity Theory   [in MathSource: Packages and Programs]
*TMecanica 1.0   [in MathSource: Packages and Programs]
Downloads Download Wolfram CDF Player

tensorial.m (18 KB) - Mathematica package
tensorial.nb (552.7 KB) - Mathematica notebook