a Mathematica package for calculations with indexed objects

About the author: Sergei A. Klioner

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What can EinS do?

EinS is a Mathematica package allowing one to perform operations with indexed objects, which may or may not be tensors. The main application field of EinS is computations with indexed objects involving implicit (Einstein) summations (EinS stands for "Einstein Summation handler"). The idea of the package was to create a simple (EinS is a relatively small package consisting of approximately 3000 lines of code), flexible package which would be easy to alter for solving any problem involving indexed objects and which would not waste time for doing anything we do not ask it to do (the latter is usual fate of the users of too general software). On the other hand, package works under Mathematica which is one of the most advanced and flexible computer algebra systems. This allows the user to employ all the power of Mathematica for solving his problem. In order to work with EinS user should have basic knowledge of the Mathematica's control structures and language. The principal features of EinS are

It was our intention to keep the package [relatively] small. The general design and functionality of EinS resulted from scientific problems in the field of astronomical applications of metric gravity theories tackled by the author during last several years. Although, the first version of EinS appeared as early as in 1994 and one can say that EinS is being developed for several years, the development of EinS is not a significant separate area of our scientific activity. That is why, a potential user should not expect that EinS is too general and flexible. For example, we did not try to implement built-in procedures for computing all standard quantities in General Relativity (curvature tensor, etc.). Moreover, the current version of EinS does not even distinguish automatically covariant and contravariant indices.

Some other systems for indicial tensor calculations:

  • ITENSOR: a standard package for Macsyma (or Maxima).
  • Stensor: a package for Macsyma (Maxima)
  • MathTensor: a package for Mathematica
  • Other systems for tensor calculations from the Computer Algebra Information Network home page.