• Corpus ID: 6688527

A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix

@article{Labahn2016AFD,
  title={A fast, deterministic algorithm for computing a Hermite Normal Form of a polynomial matrix},
  author={George Labahn and Wei Zhou},
  journal={ArXiv},
  year={2016},
  volume={abs/1602.02049}
}
Given a square, nonsingular matrix of univariate polynomials $\mathbf{F} \in \mathbb{K}[x]^{n \times n}$ over a field $\mathbb{K}$, we give a fast, deterministic algorithm for finding the Hermite normal form of $\mathbf{F}$ with complexity $O^{\sim}\left(n^{\omega}d\right)$ where $d$ is the degree of $\mathbf{F}$. Here soft-$O$ notation is Big-$O$ with log factors removed and $\omega$ is the exponent of matrix multiplication. The method relies of a fast algorithm for determining the diagonal… 
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