Fast algorithms for rational forms of integer matrices
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Computing rational forms of integer matrices
Journal of Symbolic Computation
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We consider the problem of bringing a given matrix into ''cyclic form,'' from which the rational form can be computed easily. Matrices are taken to have p-adic integer entries, and computations are done with rational integer approximations to p-adic integers. We give bounds on the precision necessary to ensure that the resulting cyclic form is indeed similar to the original matrix. We also give a criterion for deciding whether the cyclic form is correct.