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On Computing the Hermite Form of a Matrix of Differential Polynomials

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Computer Algebra in Scientific Computing (CASC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

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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 = ℚ it require time polynomial in the bit-length of the rational coefficients as well.

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Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Mark Giesbrecht & Myung Sub Kim

Authors
  1. Mark Giesbrecht
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  2. Myung Sub Kim
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Editors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

    Vladimir P. Gerdt

  2. Technische Universität München‘, Institut für Informatik, Garching, Germany

    Ernst W. Mayr

  3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2009 Springer-Verlag Berlin Heidelberg

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Giesbrecht, M., Kim, M.S. (2009). On Computing the Hermite Form of a Matrix of Differential Polynomials. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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