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\centerline{\tit {\duh EinS:} a {\itt Mathematica} Package %}
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%\centerline{\tit
for Tensorial Calculations}
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\centerline{\tit in Astronomical Applications %}
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%\centerline{\tit
of Relativistic Gravity Theories}

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\medskip

\centerline{\dh S.A.Klioner}

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\centerline{\it Institute of Applied Astronomy, 8, Zhdanovskaya st., 197042, St.Petersburg, Russia}

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\bigskip

 The package called {\dh EinS} has been implemented within {\it Mathematica}
2.2 enabling one to perform automatically complicated tensorial
calculations typical for astronomical applications of relativistic
gravitational theories. The principal features of the package are:

\item{-} Automatic handling of Einstein summations.

\item{-} Splitting time (zero-valued) and space (non
  zero-valued) indices.

\item{-} Originally developed algorithm for simplification of tensorial
  expressions is implemented accounting for the user-defined symmetries
  of tensors and renaming dummy indices. The algorithm is based on
  reducing each term into a simple canonical form (which decreases
  substantially the number of terms) and subsequent pattern matching
  among the rest of terms. This approach is proved to be more efficient
  than the algorithms based on reducing each term in a
  lexicographically minimal canonical forms used in some other
  packages.

\item{-} Standard build-in objects (the Kronecker's symbol, the Levi-Civita
  fully antisymmetric pseudotensor, a set of subroutines for computing
  standard quantities in the general theory of relativity).

\item{-} Printing tensorial expressions in "pretty" form and exporting
  them into the TeX or LaTeX forms including flexible, user-controllable
  alignment commands.

  An example of application of the package for calculation of the
Landau-Lifschits pseudotensor of the energy-momentum of gravitational
field in a rotating reference system in the first post-Newtonian
approximation is described, the resulting expressions consisting of a
few thousand terms. Physical motivation for the calculation is also
briefly discussed.

  The package is compared to the existing packages for tensorial
calculations within {\it Mathematica} (Ricci, MathTensor, etc.). Since
it is our intention to develop in the future an analogous package for
Maple, we also confront our package with the recently developed Maple
package GRTensor II.

\bye
