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Effective algorithm for computing Noetherian operators of zero-dimensional ideals

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

A Correction to this article was published on 30 August 2022

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Abstract

We consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic \({\mathcal D}\)-modules, we present a new method for computing Noetherian operators associated to a zero-dimensional ideal. An effective algorithm that consists mainly of linear algebra techniques is proposed for computing them. Moreover, as applications, new computation methods of polynomial ideals are discussed by utilizing the Noetherian operators.

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Notes

  1. Currently, the Risa/Asir implementation is in the following URL

    https://www.rs.tus.ac.jp/~nabeshima/softwares.html

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Authors and Affiliations

  1. Department of Applied Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Tokyo, Japan

    Katsusuke Nabeshima

  2. Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, Japan

    Shinichi Tajima

Authors
  1. Katsusuke Nabeshima
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  2. Shinichi Tajima
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Correspondence to Katsusuke Nabeshima.

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This work has been partly supported by JSPS Grant-in-Aid for Science Research (C) (18K03320 and 18K03214).

The original online version of this article was revised: \((\mathfrak {p}_2, \{ \partial _x\partial _y, \partial _x, \partial _y, 1\})\}\) was missed in Example 2 in PDF version. Now, it has been corrected

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Nabeshima, K., Tajima, S. Effective algorithm for computing Noetherian operators of zero-dimensional ideals. AAECC 33, 867–899 (2022). https://doi.org/10.1007/s00200-022-00570-7

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