On computing the Hermite form of a matrix of differential polynomials

Details On computing the Hermite form of a matrix of differential polynomials On computing the Hermite form of a matrix of differential polynomials

2009-06-22

arxiv.org/abs/0906.4121v1

Computer Science

Symbolic Computation

Scientific paper

Given an n x n matrix over the ring of differential polynomials F(t)[\D;\delta], 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 terms of n, deg_D(A), and deg_t(A). When F is the field of rational numbers, it also requires time polynomial in the bit-length of the coefficients.

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