Hermite form computation of matrices of differential polynomials

Hermite form computation of matrices of differential polynomials

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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 o...

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Main Author: Kim, Myung Sub
Language:en
Published: 2009
Subjects:
Symbolic Computation
Differential Algebra
Computer Science
Online Access:http://hdl.handle.net/10012/4626
id ndltd-LACETR-oai-collectionscanada.gc.ca-OWTU.10012-4626
record_format oai_dc
spelling ndltd-LACETR-oai-collectionscanada.gc.ca-OWTU.10012-46262013-10-04T04:09:08ZKim, Myung Sub2009-08-27T19:38:47Z2009-08-27T19:38:47Z2009-08-27T19:38:47Z2009-08-24http://hdl.handle.net/10012/4626Given 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.enSymbolic ComputationDifferential AlgebraHermite form computation of matrices of differential polynomialsThesis or DissertationSchool of Computer ScienceMaster of MathematicsComputer Science
collection NDLTD
language en
sources NDLTD
topic Symbolic Computation
Differential Algebra
Computer Science
spellingShingle Symbolic Computation
Differential Algebra
Computer Science
Kim, Myung Sub
Hermite form computation of matrices of differential polynomials
description 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.
author Kim, Myung Sub
author_facet Kim, Myung Sub
author_sort Kim, Myung Sub
title Hermite form computation of matrices of differential polynomials
title_short Hermite form computation of matrices of differential polynomials
title_full Hermite form computation of matrices of differential polynomials
title_fullStr Hermite form computation of matrices of differential polynomials
title_full_unstemmed Hermite form computation of matrices of differential polynomials
title_sort hermite form computation of matrices of differential polynomials
publishDate 2009
url http://hdl.handle.net/10012/4626
work_keys_str_mv AT kimmyungsub hermiteformcomputationofmatricesofdifferentialpolynomials
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