Fast parallel computation of hermite and smith forms of polynomial matrices

@article{Kaltofen1987FastPC,
  title={Fast parallel computation of hermite and smith forms of polynomial matrices},
  author={Erich L. Kaltofen and Mukkai S. Krishnamoorthy and B. David Saunders},
  journal={Siam Journal on Algebraic and Discrete Methods},
  year={1987},
  volume={8},
  pages={683-690}
}
Boolean circuits of polynomial size and polylogarithmic depth are given for computing the Hermite and Smith normal forms of polynomial matrices over finite fields and the field of rational numbers. The circuits for the Smith normal form computation are probabilistic ones and also determine very efficient sequential algorithms. Furthermore, we give a polynomial-time deterministic sequential algorithm for the Smith normal form over the rationals. The Smith normal form algorithms are applied to… 
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