Efficient decomposition of separable algebras
نویسندگان
چکیده
We present new, efficient algorithms for computations on separable matrix algebras over infinite fields. We provide a probabilistic method of the Monte Carlo type to find a generator for the centre of a given algebra A ⊆ Fm×m over an infinite field F. The number of operations used is within a logarithmic factor of the cost of solving m×m systems of linear equations. A Las Vegas algorithm is also provided under the assumption that a basis and set of generators for the given algebra are available. These new techniques yield a partial factorization of the minimal polynomial of the generator that is computed, which may reduce the cost of computing simple components of the algebra in some cases.
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عنوان ژورنال:
- J. Symb. Comput.
دوره 37 شماره
صفحات -
تاریخ انتشار 2004