Computing hermite forms of polynomial matrices

@inproceedings{Gupta2011ComputingHF,
  title={Computing hermite forms of polynomial matrices},
  author={Somi Gupta and Arne Storjohann},
  booktitle={ISSAC '11},
  year={2011}
}
This paper presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular <i>n</i> x <i>n</i> matrix <i>A</i> filled with degree <i>d</i> polynomials with coefficients from a field, the algorithm computes the Hermite form of <i>A</i> using an expected number of (<i>n</i>3<i>d</i>)<sup>1+o(1)</sup> field operations. This is the first algorithm that is both softly linear in the degree <i>d</i> and softly cubic in the dimension <i>n</i>. The algorithm is… 
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