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Quasi-stability versus Genericity

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Computer Algebra in Scientific Computing (CASC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7442))

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Abstract

Quasi-stable ideals appear as leading ideals in the theory of Pommaret bases. We show that quasi-stable leading ideals share many of the properties of the generic initial ideal. In contrast to genericity, quasi-stability is a characteristic independent property that can be effectively verified. We also relate Pommaret bases to some invariants associated with local cohomology, exhibit the existence of linear quotients in Pommaret bases and prove some results on componentwise linear ideals.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Amir Hashemi

Authors
  1. Amir Hashemi
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  2. Michael Schweinfurter
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  3. Werner M. Seiler
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Hashemi, A., Schweinfurter, M., Seiler, W.M. (2012). Quasi-stability versus Genericity. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-32973-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32972-2

  • Online ISBN: 978-3-642-32973-9

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