Tools of Tensor Calculus A.Balfagón ,P.Castellví and X.Jaén
TTC is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds. It can be of interest to the scientist working on any field where tensor calculus is needed. TTC can also be interesting for teaching purposes.


Actual version 4.3.3

     use the mouse right button
      or in ZIP-compression

If you are running Mathematica 3 to 5 take the options in the Cell menu:

Default Input FormatType = InputForm

Default Output FormatType= OutputForm

For Mathematica 6 and 7 take the options in the Edit- Preferences menu -Evaluation tab:

Default Input FormatType = RawInputForm

Default Output FormatType= OutputForm

You can enter the package using the input
In[]:= <<path/ttc.m


  • There is no restriction about the number of coordinate systems (or manifolds...) defined simultaneously, their dimension or the type of the tensor fields.
  • TTC understands both intrinsic and index notation.
  • Tensors can be expanded using coordinate or noncoordinate basis. TTC don't need orthonormal basis.
  • Basis and coordinate changes.
  • Tensor and exterior calculus: tensor product, interior product, symmetrization and antisymmetrization, exterior product, Lie and exterior derivatives.
  • Riemannian manifold computations : volume form, Hodge or star operator, Christoffel symbols, Riemann and Ricci tensors, covariant derivative, etc.
  • Utilities to save and simplify objects in TTC notation.
  • TTC can handle explicit tensor calculus ( the tensors involved are known linear combinations of a known basis) and symbolic index tensor calculus ( the tensors involded are only known through its properties like symmetries of some index and others)


We would be glad if you reference TTC in any work to which it has contributed. We would also grateful if you make us aware of your citation by sending comments or an e-mail to