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Some Notes upon “When Does \(<{\mathbb T}>\) Equal Sat \(({\mathbb T})\)?”

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Intelligent Computer Mathematics (CICM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6167))

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Abstract

Given a regular set \(\mathbb{T}\) in K[x], Lemaire et al. in ISSAC’08 give a nice algebraic property: the regular set \(\mathbb{T}\) generates its saturated ideal if and only if it is primitive. We firstly aim at giving a more direct proof of the above result, generalizing the concept of primitivity of polynomials and regular sets and presenting a new result which is equivalent to the above property. On the other hand, based upon correcting an error of the definition of U-set in AISC’06, we further develop some geometric properties of triangular sets. To a certain extent, the relation between the primitivity of \(\mathbb{T}\) and its U-set is also revealed in this paper.

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Authors and Affiliations

  1. School of Applied Mathematic, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, China

    Yongbin Li

Authors
  1. Yongbin Li
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Editor information

Editors and Affiliations

  1. German Research Center for Artificial Intelligence Bremen, Germany

    Serge Autexier

  2. Karlsruhe Institute of Technology, Germany

    Jacques Calmet

  3. CEDRIC/CNAM, Paris, France

    David Delahaye

  4. American Mathematical Society, Ann Arbor, USA

    Patrick D. F. Ion

  5. INRIA Sophia-Antipolis, France

    Laurence Rideau

  6. École Nationale Supérieure d’Informatique pour l’industrie et l’Entreprise, Evry, France

    Renaud Rioboo

  7. School of Computer Science, Edgbaston, University of Birmingham, B15 2TT, Birmingham, UK

    Alan P. Sexton

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Li, Y. (2010). Some Notes upon “When Does \(<{\mathbb T}>\) Equal Sat \(({\mathbb T})\)?”. In: Autexier, S., et al. Intelligent Computer Mathematics. CICM 2010. Lecture Notes in Computer Science(), vol 6167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14128-7_9

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  • DOI: https://doi.org/10.1007/978-3-642-14128-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14127-0

  • Online ISBN: 978-3-642-14128-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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