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On the complexity of skew arithmetic

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

In this paper, we study the complexity of several basic operations on linear differential operators with polynomial coefficients. As in the case of ordinary polynomials, we show that these complexities can be expressed almost linearly in terms of the cost of multiplication.

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Acknowledgments

The author is grateful to the second referee whose questions and remarks led to several improvements with respect to the first version of this paper. The article was originally written by the author using GNU TeXmacs, and Springer acknowledges the assistance of the author with the conversion into Springer’s LaTeX format.

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Authors and Affiliations

  1. LIX, CNRS, École Polytechnique, 91128, Palaiseau Cedex, France

    Joris van der Hoeven

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  1. Joris van der Hoeven
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Correspondence to Joris van der Hoeven.

Additional information

This work has been supported by the ANR-09-JCJC-0098-01 MaGiX Project, as well as a Digiteo 2009-36HD grant and Région Ile-de-France.

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van der Hoeven, J. On the complexity of skew arithmetic. AAECC 27, 105–122 (2016). https://doi.org/10.1007/s00200-015-0269-0

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  • DOI: https://doi.org/10.1007/s00200-015-0269-0

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