Any Hilbert space of composite dimension can be decomposed into a tensor product of Hilbert spaces of lower dimensions. Such a factorization makes it possible to decompose a quantum system into subsystems. Using a modification of quantum mechanics in which the continuous unitary group in a Hilbert space is replaced with a permutation representation of a finite group, we suggest a model for the constructive study of decompositions of a closed quantum system into subsystems. To investigate the behavior of composite systems resulting from decompositions, we develop algorithms based on methods of computer algebra and of computational group theory.
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