Computing hermite forms of polynomial matrices

Authors:
Somit Gupta;Arne Storjohann
Affiliations:
University of Waterloo, Waterloo, Canada;University of Waterloo, Waterloo, Canada
Venue:
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Year:
2011

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Abstract

This paper presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular n x n matrix A filled with degree d polynomials with coefficients from a field, the algorithm computes the Hermite form of A using an expected number of (n3d)1+o(1) field operations. This is the first algorithm that is both softly linear in the degree d and softly cubic in the dimension n. The algorithm is randomized of the Las Vegas type.