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Parametric Standard Bases and Their Applications

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Computer Algebra in Scientific Computing (CASC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11661))

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Abstract

In this paper, by stating a local variant of stability criteria due to Kalkbrener [25] and based on the Kapur et al. algorithm [30] for computing comprehensive Gröbner systems, we present an algorithm for the computation of comprehensive standard systems. Although our algorithm is a straightforward extension of the mentioned algorithm, however the effectiveness of our approach can be seen in its applications. To this end, we study some applications of parametric standard bases in catastrophe and singularity theories as well as in automated geometric theorem discovery. In particular, in the last application, it is demonstrated that for a given geometric theorem (which is not always true), our algorithm is able to construct all possible conditions under which the geometric conclusion remains locally true.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful and constructive comments.

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Authors and Affiliations

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

    Amir Hashemi & Mahsa Kazemi

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  1. Amir Hashemi
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  2. Mahsa Kazemi
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Correspondence to Amir Hashemi .

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Editors and Affiliations

  1. Coventry University, Coventry, UK

    Matthew England

  2. University of Kassel, Kassel, Germany

    Wolfram Koepf

  3. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  4. University of Kassel, Kassel, Germany

    Werner M. Seiler

  5. Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Hashemi, A., Kazemi, M. (2019). Parametric Standard Bases and Their Applications. In: England, M., Koepf, W., Sadykov, T., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2019. Lecture Notes in Computer Science(), vol 11661. Springer, Cham. https://doi.org/10.1007/978-3-030-26831-2_13

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  • DOI: https://doi.org/10.1007/978-3-030-26831-2_13

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  • Online ISBN: 978-3-030-26831-2

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