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Hermite form computation of matrices of differential polynomials

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Kim_MyungSub.pdf (475.33 KB)

Date

2009-08-27T19:38:47Z

Authors

Kim, Myung Sub

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Publisher

University of Waterloo

Abstract

Given a matrix A in F(t)[D;\delta]^{n\times n} over the ring of differential polynomials, we first prove the existence of the Hermite form H of A over this ring. Then we determine degree bounds on U and H such that UA=H. Finally, based on the degree bounds on U and H, we compute the Hermite form H of A by reducing the problem to solving a linear system of equations over F(t). The algorithm requires a polynomial number of operations in F in terms of the input sizes: n, deg_{D} A, and deg_{t} A. When F=Q it requires time polynomial in the bit-length of the rational coefficients as well.

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Keywords

Symbolic Computation, Differential Algebra

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URI

http://hdl.handle.net/10012/4626

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Computer Science