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SYMMETRICA, an object oriented computer-algebra system for the symmetric group. (English) Zbl 0823.20015

Summary: This is a review of an object oriented computer algebra system which is devoted to representation theory, invariant theory and combinatorics of the symmetric group. Moreover, it can be used for classical multivariate polynomials via the different actions of the symmetric group on the algebra of polynomials. The review contains a brief introduction to the basic methods used. Schubert polynomials are introduced, examples are given, and some applications are described. In particular, a new algorithm is provided for the evaluation of Littlewood-Richardson coefficients via symbolic computations using integer sequences instead of partitions, tableaux or lattice permutations.

MSC:

20C40 Computational methods (representations of groups) (MSC2010)
20C30 Representations of finite symmetric groups
68W30 Symbolic computation and algebraic computation
05E10 Combinatorial aspects of representation theory

Software:

SYMMETRICA
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References:

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