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GAP
GAP is a system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more. GAP is developed by international cooperation. The system, including source, is distributed freely under the terms of the GNU General Public License. You can study and easily modify or extend GAP for your special use. The current version is GAP 4, the older version GAP 3 is still available.
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Symmetrica is a program developed by Lehrstuhl Mathematik II of the University of Bayreuth. It has routines to handle the following topics: ordinary representation theory of the symmetric group and related groups, ordinary representation theory of the classical groups, modular representation theory of the symmetric group, projective representation theory of the symmetric group, combinatorics of tableaux, symmetric functions and polynomials, commutative and non commutative Schubert polynomials, operations of finite groups, ordinary representation theory of Hecke algebras of type An
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