Abstract
There are a number of problems, the solution of which requires the breakdown of the initial system of equations using algebraic decoupling methods. This means reducing the matrix of coefficients to block-diagonal (or block-triangular) form by means of substitution of variables. The main computational tasks when using such methods are finding the centralizer of several matrices or compiling the algebra generated by these matrices. For calculations, it is convenient to use the GAP computer algebra system because the system itself is designed for discrete algebra calculations. The problem is that the GAP program does not support calculations with real numbers. For practical problems you can try to replace them (with some accuracy) by rational numbers. At the same time, the decision may turn out to be excessively cumbersome. On the other hand, the advantage of GAP is the complete absence of rounding errors.
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