New system for indicial computation and its applications in gravitational physics

Abstract

EinS is a package for Mathematica intended for calculations with indexed objects (e.g. tensors). The package automatically handles dummy indices and Einstein's summation notation, enables one to define new indexed objects and to assign symmetries to that objects. EinS has an efficient simplification algorithm based on a pattern matching technique which takes full account for the symmetries of the objects and the possibility to rename dummy indices. Other important features of EinS are the ability to perform an automatically “3+1” split of implicit summations, printing expressions in a natural 2-dimensional form and exporting them into plain TEX or LATEX with user-controllable alignment commands. As a typical application of EinS, the problem of constructing of a local reference system for a massive extended body in the framework of the Parametrized Post-Newtonian formalism is briefly described. The use of EinS to solve the problem is also sketched.