within Mathematica and

its applications to metric gravity theories

**Sergei A. Klioner**

*Lorhmann Observatorium, Dresden Technical University,
Mommsenstraße 13, D-01062 Dresden, Germany*

EinS is a package for *Mathematica* intended for calculations with
indexed objects (e.g., tensors). The package automatically handles
Einstein's summation notation, generates dummy indices, enables one to
define new indexed objects and assign symmetries to that objects. EinS has an efficient simplification algorithm based on pattern matching
technique which takes full account for symmetries of the objects and
the possibility to rename dummy indices. Other important features of EinS are the ability to perform automatically "3+1" split of implicit
summations, printing expressions in a natural 2-dimensional form
and exporting into plain TEX or L^{A}TEX with user-controllable
alignment commands.

Several typical applications of EinS are described: computation of the Landau-Lifshits pseudotensor in a rotating reference system, the problem of constructing of a local reference system of a massive extended body in the framework of the parametrized post-Newtonian formalism.

IMACS ACA'98 Electronic Proceedings