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TitleEfficient decomposition of separable algebras
Author(s) W. Eberly, M. Giesbrecht
TypeArticle in Journal
AbstractWe 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 center 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.
URL http://www.sciencedirect.com/science/article/pii/S0747717103000713
JournalJournal of Symbolic Computation
Pages35 - 81
Translation No
Refereed No