On Computing the Hermite Form of a Matrix of Differential Polynomials

Authors:
Mark Giesbrecht;Myung Sub Kim
Affiliations:
Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada;Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada
Venue:
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Year:
2009

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Abstract

Given a matrix over the ring of differential polynomials, we show how to compute the Hermite form H of A and a unimodular matrix U such that UA = H . The algorithm requires a polynomial number of operations in F in terms of n , , . When F = *** it require time polynomial in the bit-length of the rational coefficients as well.