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Symbolic Computation with Indexed Objects within Mathematica
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 280-291
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A new Mathematica package EinS is intended for calculations involving sums of indexed objects (e.g., tensors). EinS automatically handles implicit summations and dummy indices, allows one to assign symmetry properties to new objects and has an efficient built-in simplification algorithm based on pattern matching. Further features include printing expressions in a 2-dimensional form, exporting into plain TeX or LaTeX with user-controllable alignment commands, converting implicit summations into explicit ones, debugging capabilities and online help messages. Some typical applications of EinSare described. 
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S. A. Klioner. Symbolic Computation with Indexed Objects within Mathematica. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 280-291. http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a14/